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Classifications of commutative Banach algebras and Banach modules

Research Project

Project/Area Number 08640160
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field 解析学
Research InstitutionYamagata University

Principal Investigator

TAKAHASI Sin-Ei  Yamagata University Faculty of Enginnering Professor, 工学部, 教授 (50007762)

Co-Investigator(Kenkyū-buntansha) HATORI Osamu  Niigata University Graduate School of Science and Technology Associate Professor, 大学院・自然科学研究科, 助教授 (70156363)
Project Period (FY) 1996 – 1997
Project Status Completed (Fiscal Year 1997)
Budget Amount *help
¥2,000,000 (Direct Cost: ¥2,000,000)
Fiscal Year 1997: ¥900,000 (Direct Cost: ¥900,000)
Fiscal Year 1996: ¥1,100,000 (Direct Cost: ¥1,100,000)
Keywordscommutative Banach algebra / BSE-algbera / Segal algebra / Apostol algbera / Douglas algebra / Gelfand transform / Fourier transform / bounded approximate identity / commutative Banach algebra / Douglas algebra / Fourier transtorm / commutafivc Banach algcbra / grcatcst regular closed subalgebra / boundcd approximatc identiy
Research Abstract

Classifications are based on setting several conditions and considering the classes to satisfy the conditions. This research has been focusing on clarifying the essence of commutative Banach algebras and Banach modules by the following idea : First, they would be classified according to the natural conditions settled, and then whether concrete algebras and modules belong to the classified groups or not, and what invariant properties the specific classified algebra and module have, might be investigated. Before this investigation, based on the above idea we have introduced and investigated the groups respective to BSE-algebras and BSE-Banach modules. In this investigation, we have introduced the new group of commutative Banach algebras named Doss-algebras and developed the general classification theory of the commutative Banach algebras. This general classification theory was based on newly introduced concept referred to quasi-topology. Then, whether the concrete commutative Banach algebras belong to the above two groups respective to the BSE-algebras and the Doss-algebras has been investigated. Furthermore, we have studied on the group of commutative Banach algebras such that the original norm coincides with the BSE-norm and on a certain group of BSE-Banach modules.
We have also studied on the group of the commutative Banach algebras of which the greatest regular subalgebra coincides with the Apostol algebras and particularly it is found that the Douglas algebra belongs to such a group and has a certain decomposition based on the natural spectra. In the study of the function which operates on the function space related to the commutative Banach algebra, non-Lipschitz functions which operate or do not operate on non-trivial function space can be characterized successfully. Finally, we have investigated a structure of ring-homomorphism on the commutative Banach algebras, inequality and equality with respect to the Banach norm, and a BKW-operator.

Report

(3 results)
  • 1997 Annual Research Report   Final Research Report Summary
  • 1996 Annual Research Report
  • Research Products

    (86 results)

All Other

All Publications (86 results)

  • [Publications] Ryotaro Sato: "A discrete Korovkin theorem and BKW-operators" Journal of Approximation Theory. 84-3. 351-366 (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] Sin-Ei Takahasi: "A generalized Fourier transformation for Lp(G)-modules" Mathematica Japonica. 44-1. 55-59 (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] Sin-Ei Takahasi: "Bohman-Korovkin-Wulbert operators from a function space into a commutative C^*-algebra for special test functions" Tohoku Mathematical Journal. 48. 139-148 (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] Keiji Izuchi: "BKW-operators on the interval and the sequence spaces" Journal of Approximation Theory,. 87-2. 159-169 (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] Sin-Ei Takahasi: "Korovkin type approximation theorems I" RIMS Kokyuroku. 946. 1-9 (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] Makoto Tsukada: "On the Nakamura-Schweitzer-Kantrovich inequality" RIMS Kokyuroku. 975. 116-122 (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] 高橋 眞映: "Jensenの逆不等式とその応用" Hokkaido Univ.Technical Report Series in Mathematics. 48. 66-68 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] Sin-Ei Takahasi: "Commutative Banach algebras and BSE-norm" Mathematica Japonica. 46-2. 273-277 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] Keiji Izuchi: "BKW-operators on the interval[0,1]" Rendconti del Circolo Matematico di Palermo(2). 46. 477-489 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] Makoto Tsukada: "The best possibility of the bound for the Kantrovich inequality and some remarks" Journal of Inequalies and Applications. 1. 327-334 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] Masatoshi Fujii: "Operator inequalities and covariance in noncommutative probability" Mathematica Japonica. 46-2. 317-320 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] Sin-Ei Takahasi: "A generalization of the Alzer-Faiziev inequality" Utilitas Mathematica. 51. 3-8 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] Sin-Ei Takahasi: "可換C^*-環上の環準同型写像の構造に関する一考察" RIMS Kokyuroku. 979. 115-119 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] Osamu Hatori: "On the greatest regular closed subalgebras and the Apostol algberas of Lp-multipliers whose Fourier transforms are continuous and vanish at infinity" Tokyo Journal of Mathematics. 20-2. 453-462 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] Sin-Ei Takahasi: "A Hlawka type inequality and its converse" Hokkaido Univ.Technical Report Series in Mathematics. 52. 42-45 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] Sin-Ei Takahasi: "A structure of ring homomorphisms on commutative Banach algebras" Proceedings of the American Mathematical Society. (近刊).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] Takuya Hara: "A refinement of various mean inequalities" Journal of Inequalities and Applications. (近刊).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] Sin-Ei Takahasi: "An inverse type of Jensen's inequality" Mathematica Japonica. (近刊).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] Ritsuo Nakamoto: "Generalizations of an inequality of Marcus" Mathematica Japonica. (近刊).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] Sin-Ei Takahasi: "Jensenの逆不等式の等号成立条件" RIMS Kokyuroku. (近刊).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] Sin-Ei Takahasi: "Some convexity constants related to Hlawka inequalities in Banach spaces" RIMS Kokyuroku. (近刊).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] Sin-Ei Takahasi: "The proximinality of the center of a quasicentral C^*-algebra" RIMS Kokyuroku. (近刊).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] Osamu Hatori: "Measures with natural spectra on locally compact abelian groups" Proceeding of the Americal Mathematical Society. (近刊).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] Osamu Hatori: "Apostol algebras and decomposition in Douglas algberas" Michigan Mathematical Journal. (近刊).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] Osamu Hatori: "Non-Lipschitz functions which operate on function spaces" Mathematica Japonica. (近刊).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] Osamu Hatori: "有限領域上のShapiro-Shields型定理" RIMS Kokyuroku. (近刊).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] Ryotaro Sato: "A discrete Korovkin theorem and BKW-operators" Journal of Approximation Theory. 84-3. 351-366 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] Sin-Ei Takahasi: "A generalized Fourier transformation for L^p (G)-modules" Mathematica Japonica. 44-1. 55-59 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] Sin-Ei Takahasi: "Bohman-Korovkin-Wulbert operators from a function space into a commutative C^<**>-algebra for special test functions" Tohoku Mathematical Journal. 48. 139-148 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] Keiji Izuchi: "BKW-operators on the interval and the sequence spaces" Journal of Approximation Theory. 87-2. 159-169 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] Sin-Ei Takahasi: "Korovkin type approximation theorems, I" RIMS Kokyuroku. 946. 1--9 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] Makoto Tsukada: "On the Nakamura-Schweitzer-Kantrovich inequality" RIMS Kokyuroku. 975. 116-122 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] Sin-Ei Takahasi: "Jensen's inequality and its applications" Hokkaido Univ.Technical Report Series in Mathematics. 48. 66-68 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] Sin-Ei Takahasi: "Commutative Banach algebras and BSE-norm" Mathematica Japonica. 46-2. 273-277 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] Keiji Izuchi: "BKW-operators on the interval [0,1]" Rendconti del Circolo Matematico di Palermo (2). 46. 477-489 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] Makoto Tsukada: "The best possibility of the bound for the Kantrovich inequality and some remarks" Journal of Inequalies and Applications. 1. 327-334 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] Masatoshi Fujii: "Operator inequalities and covariance in noncommutative probability" Mathematica Japonica. 46-2. 317-320 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] Sin-Ei Takahasi: "A generalization of the Alzer-Faiziev inequality" Utilitas Mathematica. 51. 3-8 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] Sin-Ei Takahasi: "On a structure of ring-homomorphisms on commutative C^<**>-algberas" RIMS Kokyuroku. 979. 115-119 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] Osamu Hatori: "On the greatest regular closed subalgebras and the Apostol algberas of L^p-multipliers whose Fourier transforms are continuous and vanish at infinity" Tokyo Journal of Mathematics. 20-2. 453-462 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] Sin-Ei Takahasi: "A Hlawka type inequality and its converse" Hokkaido Univ.Technical Report Series in Mathematics. 52. 42-45 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] Sin-Ei Takahasi: "A structure of ring homomorphisms on commutative Banach algebras" Proceedings of the American Mathematical Society.(to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] Takuya Hara: "A refinement of various mean inequalities" Journal of Inequalities and Applications.(to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] Sin-Ei Takahasi: "An inverse type of Jensen's inequality" Mathematica Japonica.(to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] Ritsuo Nakamoto: "Generalizations of an inequality of Marcus" Mathematica Japonica.(to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] Sin-Ei Takahasi: "A condition for the equality of Jensen's inequality" RIMS Kokyuroku.(to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] Sin-Ei Takahasi: "Some convexity constants related to Hlawka inequalities in Banach spaces" RIMS Kokyuroku.(to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] Sin-Ei Takahasi: "The proximinality of the center of a quasicentral C^<**>-algebra" RIMS Kokyuroku.(to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] Osamu Hatori: "Measures with natural spectra on locally compact abelian groups" Proceeding of the Americal Mathematical Society.(to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] Osamu Hatori: "Apostol algebras and decomposition in Douglas algberas" Michigan Mathematical Journal.(to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] Osamu Hatori: "Non-Lipschitz functions which operate on function spaces" Mathematica Japonica. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] Osamu Hatori: "Shapiro-Shields type theorem on finitedomain" RIMS Kokyuroku.(to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] Sin-Ei Takahasi: "Commutative Banach algebras and BSE-norm" Mathematica Japonica. 46-2. 273-277 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] Keiji Izuchi: "BKW-operators on the interval" Rendconti del Circolo Matematico di Palermo (2). 46. 477-489 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] Makoto Tsukada: "The best possibility of the bound for the Kantrovich inequality and some remarks" Journal of Inequalies and Applications. 1. 327-334 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] Masatoshi Fujii: "Operator inequalities and covariance in noncommutative probability" Mathematica Jaonica. 46-2. 317-320 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] Sin-Ei-Takahasi: "A generalization of the Alzer-Faiziev inequality" Utilitas Mathematica. 51. 3-8 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] Sin-Ei-Takahasi: "可換C^*-環上の環準同型写像の構造に関する一考察" RIMS Kokyuroku. 979. 115-119 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] Osamu Hatori: "On the greatest regular closed subalgebras and the Apostol algberas of L^p-multipliers whose Fourier transforms are continuous and vanish at infinity" Tokyo Journal of Mathematics. 20-2. 453-462 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] Sin-Ei-Takahasi: "A Hlawka type inequality and its converse" Hokkaido Univ. Technical Report Series in Mathematics. 52. 42-45 (1998)

    • Related Report
      1997 Annual Research Report
  • [Publications] Sin-Ei-Takahasi: "A structure of ring homomorphisms on commutative Banach algebras" Proceedings of the American Mathematical Society. (近刊).

    • Related Report
      1997 Annual Research Report
  • [Publications] Takuya Hara: "A refinement of various mean inequalities" Journal of Inequalities and Applications. (近刊).

    • Related Report
      1997 Annual Research Report
  • [Publications] Sin-Ei-Takahasi: "An inverse type of Jensen′s inequality" Mathematica Japonica. (近刊).

    • Related Report
      1997 Annual Research Report
  • [Publications] Ritsuo Nakamoto: "Generalizations of an inequality of Marcus" Mathematica Japonica. (近刊).

    • Related Report
      1997 Annual Research Report
  • [Publications] Sin-Ei-Takahasi: "Jensenの逆不等式の等号成立条件" RIMS Kokyuroku. (近刊).

    • Related Report
      1997 Annual Research Report
  • [Publications] Sin-Ei-Takahasi: "Some convexity constants related to Hlawka inequalities in Banach spaces" RIMS Kokyuroku. (近刊).

    • Related Report
      1997 Annual Research Report
  • [Publications] Sin-Ei-Takahasi: "The proximinality of the center of a quasicentral C^*-algebra" RIMS Kokyuroku. (近刊).

    • Related Report
      1997 Annual Research Report
  • [Publications] Osamu Hatori: "Measures with natural spectra on locally compact abelian groups" Proceeding of the Americal Mathematical Society. (近刊).

    • Related Report
      1997 Annual Research Report
  • [Publications] Osamu Hatori: "Apostol algebras and decomposition in Douglas algberas" Michigan Mathematical Journal. (近刊).

    • Related Report
      1997 Annual Research Report
  • [Publications] Osamu Hatori: "Non-Lipschitz functions which operate on function spaces" Mathematica Japonica. (近刊).

    • Related Report
      1997 Annual Research Report
  • [Publications] Osamu Hatori: "有限領域上のShapiro-Shields型定理" RIMS Kokyuroku. (近刊).

    • Related Report
      1997 Annual Research Report
  • [Publications] Ryotaro Sato: "A discrete Korovkin theorem and BKW-operators" Journal of Approximation Theory. 84-3. 351-366 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] Sin-Ei Takahasi: "A generalized Fourier transformation for L^F(G)-modules" Mathematica Japonica. 44-1. 55-59 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] Sin-Ei Takahasi: "Bohman-Korovkin-Wulbert operators from a function space into a commutative C^*-algebra for special test functions" Tohoku Mathematical journal. 48. 139-148 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] Keiji Izuchi: "BKW-operators on the interval and the sequence spaces" Journal of Approximation Theory. 87-2. 159-169 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] Sin-Ei Takahasi: "Korovkin type approximation theorems I" RIMS Kokyuroku. 946. 1-9 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] Makoto Tsukada: "On the Nakamura-Schweitzer-Kantrovich inequality" RIMS Kokyuroku. 947. 116-122 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] 高橋眞映: "Jensenの逆不等式とその応用" Hokkaido Univ,Technical Report Series in Mathenatics. 48. 66-68 (1997)

    • Related Report
      1996 Annual Research Report
  • [Publications] Sin-Ei Takahasi: "Commutative Banach algebras and BSE-norm" Mathematica Japonica. (近刊).

    • Related Report
      1996 Annual Research Report
  • [Publications] Keiji Izuchi: "BKW-operators on the interval" Rendconti del Circolo Matematico di Palermo (2). (近刊).

    • Related Report
      1996 Annual Research Report
  • [Publications] Makoto Tsukada: "The best possibility of the bound for the Kantrovich inequality and some remarks" Journal of Inequalies and Applications. (近刊).

    • Related Report
      1996 Annual Research Report
  • [Publications] Masatoshi-Fujii: "Operator inequalities and covariance in noncommutative probability" Mathematica Japonica. (近刊).

    • Related Report
      1996 Annual Research Report
  • [Publications] Sin-Ei Takahasi: "A gcneralization of the Alzer-Faiziev inequality" Utikitas Mathematica. (近刊).

    • Related Report
      1996 Annual Research Report
  • [Publications] Sin-Ei Takahasi: "可換C^*-環上の環準同型写像の構造に関する一考察" RIMS Kokyuroku. (近刊).

    • Related Report
      1996 Annual Research Report
  • [Publications] Osamu Hatori: "On the greatcst regular closed subalgebras and the Apostol algberas of L^F-multipliers whose Fourier transforms are continuous and vanish at infinity" Tokyo Journal of Mathematics. (近刊).

    • Related Report
      1996 Annual Research Report
  • [Publications] Osamu Hatori: "Measure with natural spectra on locally compact abelian groups" Proceeding of the Americal Mathematical Society. (近刊).

    • Related Report
      1996 Annual Research Report

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Published: 1996-04-01   Modified: 2016-04-21  

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