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Research on automatic linearities for ring homomorphisms on commutative Banach algebras

Research Project

Project/Area Number 14540161
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Basic analysis
Research InstitutionNIIGATA UNIVERSITY

Principal Investigator

HATORI Osamu  NIIGATA UNIVERSITY, Faculty of Science, Rrofessor, 理学部, 教授 (70156363)

Co-Investigator(Kenkyū-buntansha) WATANABE Keiichi  NIIGATA UNIVERSITY, Faculty of Science, Associate Rrofessor, 理学部, 助教授 (50210894)
SAITO Kichi-suke  NIIGATA UNIVERSITY, Faculty of Science, Rrofessor, 理学部, 教授 (30018949)
IZUCHI Keiji  NIIGATA UNIVERSITY, Faculty of Science, Rrofessor, 理学部, 教授 (80120963)
MIURA Takeshi  Yamagata University, International Student Center, Associate Rrofessor, 留学生センター, 助教授 (90333989)
TAKAHASI Sin-ei  Yamagata University, Faculty of Engineering, Rrofessor, 工学部, 教授 (50007762)
Project Period (FY) 2002 – 2003
Project Status Completed (Fiscal Year 2003)
Budget Amount *help
¥3,200,000 (Direct Cost: ¥3,200,000)
Fiscal Year 2003: ¥1,600,000 (Direct Cost: ¥1,600,000)
Fiscal Year 2002: ¥1,600,000 (Direct Cost: ¥1,600,000)
Keywordscommutative Banach algebra / ring homomorphism / composition operator / Composition operator
Research Abstract

Although it is natural in considering the map on a Banach ring to consider the map(homomorphism) which saves three operations, the ring homomorphism which does not assume preservation of scalar multiplication is sometimes often linear automatically. It considered what case aring homomorphism would turn into an linear map automatically. An representation theorem of the ring homomorphism on a commutative Banach algebra was proved. When the conditions which many commutative Banach algebras fulfill were assumed, it was shown that a ring homomorphism can be represented using the continuation map on the maximum ideal space and the ring homomorphism on a complex number field, and it gave that the ring homomorphism on commutative Banach algebras which contain an element whose spectrum is large using this turned into a linear map. It was shown that especially the ring homomorphism on a disk algebra is complex-linear or conjugate-complex linear, if the non-constant function is contained in the r … More ange. Moreover, a necessary and sufficient condition for a Banach algebra to be of a finite dimension was given using the language of the Banach algebra-valued simultaneous polynomial. Among the composition operators on the Banach algebra of all bounded analytic functions on the unit disk we considered the both cases that a given composition operator is isolated and in an essential component. Moreover, we considered ideals of which closures are intersections of maximal ideals of the Banach algebra of all bounded analytic functions on the disk. It was shown that the ring homomorphism to a real commutative Banach algebra in a narrow sense from a real commutative Banach algebra can be represented by a continuous function of a certain kind between the maximal ideal spaces. Moreover, we considered the division problem. Moreover, we considered the closed ideal generated by one outer function. Moreover, the characterization for absolute norm on complex Euclidian space being smooth was given. The Wirtinger type inequality relevant to an elliptic differential equation and the inequality of Beesack said for relation to be in differential geometry were discussed systematically. It extended to the case of Banach space-valued function. Essential norm and Hyers-Ulam stability constant of a weighted composition operator on C (X) described completely in the language of a certain kind of the same level set. Less

Report

(3 results)
  • 2003 Annual Research Report   Final Research Report Summary
  • 2002 Annual Research Report
  • Research Products

    (74 results)

All Other

All Publications (74 results)

  • [Publications] Osamu Hatori: "Characterizations and automatic linearity for ring homomorphisms on algebras of functions"Contemp.Math.. 328. 201-215 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Keiji Izuchi: "K-hulls of QC-level sets"Indiana Univ.Math.. 52・2. 421-436 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] P.Gorkin: "Sequences separating fibers in the spectrum of H^∞"Topology Appl.. 129・3. 221-238 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Kichi-Suke Saito: "Uniform convexity of ψ-direct sums of Banach spaces"Journal of Mathematical Analysis and Applications. 277. 1-11 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Mikio Kato: "On ψ-direct sums of Banach spaces and convexity"Journal of the Australian Mathematical Society. 75. 413-422 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] K.Mitani: "Smoothness of absolute norms on C^n"J.Convex Analysis. 10. 89-107 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] K.Mitani: "The James constant of absolute norms on R^2"Journal of Nonlinear and Convex Analysis. 4. 399-410 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Takeshi Miura: "A characterization of Hyers-Ulam stability of first order linear Differential operators"J.Math.Anal.Appl.. 289. 136-146 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Sin-Ei Takahasi: "On the structure of the solution set of a third kind boundary value problem"Math.Nachr.. 257. 99-107 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Sin-Ei Takahasi: "A note on Wirtinger-Beesack's inequality"Math.Inequal.Appl.. 6・2. 277-282 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Takeshi Miura: "Ring homomorphisms on real Banach algebras"Internat.J.Math.and Math.Sci.. 48. 3025-3029 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Takuya Hara: "On weighted extensions of Carleman's inequality and Hardy's inequality"Math.Inequal.Appl.. 6・4. 667-674 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Takeshi Miura: "Hyers-Ulam stability of linear differential operator with constant coefficients"Math.Nachr.. 258. 90-96 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Hiroyuki Takagi: "Essential norm and stability constant of weighted composition operators on C(X)"Bill.Korean Math.Soc.. 40・4. 583-591 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Sin-Ei Takahasi: "A note on a class of Banach algebra-valued polynomials"Int.J.Math.Math.Sci.. 32・3. 189-192 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] K.Izuchi: "Outer and inner vanishing measures and division in H^∞ +C"Rev.Mat.Iberoamericana. 18・3. 511-540 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] K.Izuchi: "On ideals in H wh^∞ ose closures are intersections of maximal ideals"Michigan Math.J.. 50・1. 3-16 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] T.Hosokawa: "Isolated points and essential components of composition operators on H^∞"Proc.Amer.Math.Soc.. 130・6. 1765-1773 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Yasuji Takahashi: "Strict convexity of absolute norms on C^2 and direct sums of Banach spaces"Journal of Inequalities and Applications. 7. 179-186 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Hiroyuki Takagi: "Polynomial idendities that imply commutativeity of rings"Linear Algebra Appl.. 341. 299-307 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Yasuji Takahashi: "Some convexity constants related to Hlawka type inequalities in Banach spaces"J.Inequal.Appl.. 7・1. 125-141 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Sin-Ei Takahasi: "On the Hyers-Ulam stability of the Banach space-valued differential Equation y'=λy"Bull.Korean Math.Soc.. 39・2. 309-315 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Takeshi Miura: "A representation of ring homomorphisms on unital regular commutaitve Banach algebras"Math.Jour.Okayama Univ.. 44. 143-153 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Osamu Hatori: "Characterizations and automatic linearity for ring homomorphisms on algebras of functions"Contemp.Math.. 328. 201-215 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Keiji Izuchi: "K-hulls of QC-level sets"Indiana Univ.Math.. 52. 421-436 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] P.Gorkin: "Swquences separating fibers in the spectrum of H^∞"Topology Appl.. 129. 221-238 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Kichi-Suke Saito: "Uniform convexity of Ψ-direct sums of Banach spaces"Jour.Math.Anal.Appl.. 277. 1-11 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Mikio Kato: "On Ψ-direct sums of Banach spaces and convexity"Jour.Australian Math.Soc.. 75. 412-422 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] K.Mitani: "Smoothness of absolute norms on C^n"Jour.Convex Anal.. 10. 89-107 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] K.Mitani: "The James constant of absolute norms on R^2"Jour.Nonlinear and Convex Anal.. 4. 399-410 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Takeshi Miura: "A characterization of Hyers-Ulam stability of first order linear differential operators"Jour.Math.Anal.Appl.. 286. 136-146 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Sin-Ei Takahasi: "On the structure of the solution set of a third kind boundary value problem"Math.Nachr.. 257. 99-107 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Sin-Ei Takahasi: "A note on Wirtinger-Beesack's inequality"Math.Inequal.Appl.. 6. 277-282 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Takeshi Miura: "Ring homomorphisms on real Banach algebras"Intemat.Jour.Math.Math.Sci.. 48. 3025-3029 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Takuya Hara: "On weighted extensions of Carleman's inequality and Hardy's inequality"Math.Inequal.Appl.. 6. 667-674 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Takeshi Miura: "Hyers-Ulam stability of linear differential operator with constant coefficients"Math.Nachr.. 258. 90-96 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Hiroyuki Takagi: "Essential norm and stability constant of weighted composition operators on C(X)"Bull.Korean Math.Soc.. 40. 583-591 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Sin-Ei Takahasi: "A note on a class of Banach algebra-^valued polynomials"Internat.Jour.Math.Math.Sci.. 32. 189-192 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] K.Izuchi: "Outer and inner vanishing measures and division in H^∞+C"Rev.Math.Iberoamericana. 18. 511-540 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] K.Izuchi: "On ideals in H^∞ whose closures are intersectins of maximal ideals"Michigan Math.Jour.. 50. 3-16 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] T.Hosokawa: "Isolated points and essential components of composition operators on H^∞"Proc.Amer.Math.Soc.. 130. 1765-1773 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Yasuji Takahasi: "Strict convexity of absolute notms on C^2 and direct sums of Banach spaces"Jour.Ineq.Appl.. 7. 179-186 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Hiroyuki Takagi: "Polynomial identities that imply commutativity of rings"Linear Algebra Appl.. 341. 299-307 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Yasuji Takahasi: "Some convexity constants related to Hlawka type inequalities in Banach spaces"Jour.Inequal.Appl.. 7. 125-141 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Sin-Ei Takahasi: "On the Hyers-Ulam stability of the Banach space-valued differential equation y'=λy"Bull.Korean Math.Soc.. 39. 309-315 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Takeshi Miura: "A representation of ring homomorphisms on unital regular commutaitve Banach algebras"Math.J.Okayama Univ.. 44. 143-153 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Osamu Hatori: "Characterizations and automatic linearity for ring homomorphisms on algebras of functions"Contemp.Math.. 328. 201-215 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] Keiji Izuchi: "K-hulls of QC-level sets"Indiana Univ.Math.. 52・2. 421-436 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] P.Gorkin: "Sequences separating fibers in the spectrum of H^∞"Topology Appl.. 129・3. 221-238 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] K.Izuchi: "Common zero sets of equivalent singular inner functions"Studia Math.. 発表予定.

    • Related Report
      2003 Annual Research Report
  • [Publications] K.Izuchi: "Non-analytic sets and QC-level sets in the maximal ideal space of H^∞"Rocky Mount.J.Math.. 発表予定.

    • Related Report
      2003 Annual Research Report
  • [Publications] K.Izuchi: "Norm closed invariant spaces in L^∞ and H^∞"Glasgow Math.J.. 発表予定.

    • Related Report
      2003 Annual Research Report
  • [Publications] K.Izuchi: "Backward shift invariant subspaces in the bidisc"Hokkaido Math.J.. 発表予定.

    • Related Report
      2003 Annual Research Report
  • [Publications] K.Izuchi: "Backward shift invariant subspaces in the bidisc II"J.Operator Theory. 発表予定.

    • Related Report
      2003 Annual Research Report
  • [Publications] K.Izuchi: "The structure of the maximal ideal space of H^∞"Sugaku Expositions. 発表予定.

    • Related Report
      2003 Annual Research Report
  • [Publications] J.S.Choa: "A note on maximal inner spaces of the Bergman space"Integral Eq.Op.Th.. 発表予定.

    • Related Report
      2003 Annual Research Report
  • [Publications] K.Izuchi: "Strictly contractive compression on backward shift invairant subspaces over the torus"Acta Sci.Math.(Szeged). 発表予定.

    • Related Report
      2003 Annual Research Report
  • [Publications] Kichi-Suke Saito: "Uniform convexity of ψ-direct sums of Banach spaces"Journal of Mathematical Analysis and Applications. 277. 1-11 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] Mikio Kato: "On ψ-direct sums of Banach spaces and convexity"Journal of the Australian Mathematical Society. 75. 413-422 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] K.Mitani: "Smoothness of absolute norms on C^n"J.Convex Analysis. 10. 89-107 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] K.Mitani: "The James constant of absolute norms on R^2"Journal of Nonlinear and Convex Analysis. 4. 399-410 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] Mikio Kato: "Uniform non-squareness of ψ-direct sums of Banach spaces 【symmetry】ψY"Mathematical Inequalities and Applications. 発表予定.

    • Related Report
      2003 Annual Research Report
  • [Publications] Takeshi Miura: "A characterization of Hyers-Ulam stability of first order linear Differential operators"J.Math.Anal.Appl.. 286. 136-146 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] Sin-Ei Takahasi: "On the structure of the solution set of a third kind boundary value problem"Math.Nachr.. 257. 99-107 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] Sin-Ei Takahasi: "A note on Wirtinger-Beesack's inequality"Math.Inequal.Appl.. 6・2. 277-282 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] Takeshi Miura: "Ring homomorphisms on real Banach algebras"Internat.J.Math.and Math.Sci.. 48. 3025-3029 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] Takuya Hara: "On weighted extensions of Garleman's inequality and Hardy's inequality"Math.Inequal.Appl.. 6・4. 667-674 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] Takeshi Miura: "Hyers-Ulam stability of linear differential operator with constant coefficients"Math.Nachr.. 258. 90-96 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] Hiroyuki Takagi: "Essential norm and stability constant of weighted composition operators on C(X)"Bull.Korean Math.Soc.. 40・4. 583-591 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] O.Hatori: "Characterizations and automatic linearity for ring homomorphisms on algebras of functions"Contemporary Mathematics. (発表予定).

    • Related Report
      2002 Annual Research Report
  • [Publications] S.E.Takahashi: "A note on class of Banach algebra-valued polynomials"Internat. Jour. Math. and Math. Sci.. 32・3. 189-192 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] T.Hosokawa: "Isolated points and essential components of composition operators on H^∞"Proc. Amer. Math. Soc.. 130・6. 1765-1773 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] K.Izuchi: "On ideals in H^∞ whose closures are intersections of maximal ideals"Michigan Math. J.. 50・1. 3-16 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] K.Saito: "Uniform convexity of 4-direct sum of Banach spaces"J. Math. Anal. Appl.. 277・1. 1-11 (2003)

    • Related Report
      2002 Annual Research Report

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Published: 2002-04-01   Modified: 2016-04-21  

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