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Spectrum preservers on Banach algebras and the stability of their perturbation

Research Project

Project/Area Number 23740097
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeMulti-year Fund
Research Field Basic analysis
Research InstitutionNiigata University (2013-2014)
Yamagata University (2011-2012)

Principal Investigator

MIURA TAKESHI  新潟大学, 自然科学系, 教授 (90333989)

Project Period (FY) 2011-04-28 – 2015-03-31
Project Status Completed (Fiscal Year 2014)
Budget Amount *help
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2014: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2013: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2012: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2011: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Keywordsスペクトル保存写像 / 等距離写像 / 関数環 / 可換Banach環 / 摂動の安定性 / スペクトル保存
Outline of Final Research Achievements

I investigated the structure of mappings which preserve spectra or related information between Banach algebras in detail. I gave a characterization of surjective isometries without assuming linearity between function algebras, which need not be unital. Many results on multiplicatively peripheral spectrum preserving surjections are well known. I generalized some of them and proved the structure theorem on spectra radii preserving mappings between unital semi-simple commutative Banach algebras. I gave a necessary and sufficient condition for a system of Banach space valued differential equations to be stable in the sense of Hyers and Ulam. I also gave a sufficient condition for an integral equation to have the Hyers-Ulam stability.

Report

(5 results)
  • 2014 Annual Research Report   Final Research Report ( PDF )
  • 2013 Research-status Report
  • 2012 Research-status Report
  • 2011 Research-status Report
  • Research Products

    (31 results)

All 2015 2014 2013 2012 2011 Other

All Journal Article (18 results) (of which Peer Reviewed: 15 results,  Open Access: 2 results,  Acknowledgement Compliant: 1 results) Presentation (13 results) (of which Invited: 6 results)

  • [Journal Article] Real-linear isometries between subspaces of continuous functions2014

    • Author(s)
      H. Koshimizu, T. Miura, H. Takagi and S.-E. Takahasi
    • Journal Title

      J. Math. Anal. Appl.

      Volume: 413 Issue: 1 Pages: 229-241

    • DOI

      10.1016/j.jmaa.2013.11.050

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Ulam type stability problems for alternative homomorphisms2014

    • Author(s)
      S.-E. Takahasi, M. Tsukada, T. Miura, H. Takagi and K. Tanahashi
    • Journal Title

      J. Inequal. Appl.

      Volume: 2014:228

    • NAID

      120007101195

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] Ulam typw stability of a generalized additive mapping and concrete examples2013

    • Author(s)
      H. Oda, M. Tsukada, T. Miura, Y. Kobayashi and S.-E. Takahasi
    • Journal Title

      Int. J. Math. Math. Sci.

      Volume: 2013 Pages: 1-7

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] A characterization of the stability of a system of the Banach space valued differential equations2013

    • Author(s)
      T. Miura, G. Hirasawa S.-E. Takahasi and T. Hayata
    • Journal Title

      Math. Inequal. Appl.

      Volume: 16 Issue: 3 Pages: 717-728

    • DOI

      10.7153/mia-16-54

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] Real linear isometries between function algebras. II2013

    • Author(s)
      Osamu Hatori and Takeshi Miura
    • Journal Title

      Cent. Eur. J. Math.

      Volume: 11 Issue: 10 Pages: 1838-1842

    • DOI

      10.2478/s11533-013-0282-0

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] Ulam type stability of a generalized additive mapping and concrete examples2013

    • Author(s)
      Hiroyoshi Oda, Makoto Tsukada, Takeshi Miura, Yuji Kobayashi and Sin-Ei Takahasi
    • Journal Title

      Int. J. Math. Math. Sci.

      Volume: 2013

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] A note on the stability of an integral equation2012

    • Author(s)
      Takeshi Miura, Go Hirasawa, Sin-Ei Takahasi and Takahiro Hayata
    • Journal Title

      Functional Equations in Mathematical Analysis

      Volume: 52 Pages: 207-222

    • DOI

      10.1007/978-1-4614-0055-4_17

    • ISBN
      9781461400547, 9781461400554
    • Related Report
      2012 Research-status Report
  • [Journal Article] The Hyers-Ulam and Ger type stabilities of the first order linear differential equations2012

    • Author(s)
      Takeshi Miura and Go Hirasawa,
    • Journal Title

      Functional Equations in Mathematical Analysis

      Volume: 52 Pages: 191-199

    • DOI

      10.1007/978-1-4614-0055-4_15

    • ISBN
      9781461400547, 9781461400554
    • Related Report
      2012 Research-status Report
  • [Journal Article] On the Butler-Rassias functional equation and its generalized Hyers-Ulam stability2012

    • Author(s)
      Takeshi Miura, Go Hirasawa and Takahiro Hayata
    • Journal Title

      Functional Equations in Mathematical Analysis

      Volume: 52 Pages: 201-206

    • DOI

      10.1007/978-1-4614-0055-4_16

    • ISBN
      9781461400547, 9781461400554
    • Related Report
      2012 Research-status Report
  • [Journal Article] Reflections and a generalization of the Mazur-Ulam theorem2012

    • Author(s)
      Osamu Hatori, Kiyotaka Kobayashi, Takeshi Miura and Sin-Ei Takahasi
    • Journal Title

      Rocky Mountain J. Math.

      Volume: 42 Issue: 1

    • DOI

      10.1216/rmj-2012-42-1-117

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] Stability of the Banach space valued Chebyshev differential equation2012

    • Author(s)
      Takeshi Miura, Sin-Ei Takahasi, Takahiro Hayata and Kotaro Tanahashi
    • Journal Title

      Appl. Math. Lett.

      Volume: 25 Issue: 11 Pages: 1976-1979

    • DOI

      10.1016/j.aml.2012.03.012

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] Stability problems for generalized additive mappings and Euler-Lagrange type mappings2012

    • Author(s)
      Mamoru Todoroki, Keisaku Kumahara, Takeshi Miura and Sin-Ei Takahasi
    • Journal Title

      Aust. J. Math. Anal. Appl.

      Volume: 9

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] Isometries and translations of groups2012

    • Author(s)
      Osamu Hatori, Go Hirasawa, Takeshi Miura and Lajos Molnar
    • Journal Title

      Tokyo J. Math.

      Volume: 35

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] An equality condition of Arhippainen-Muller's estimate and its related problem2011

    • Author(s)
      S.-E. Takahasi, T. Miura and T. Hayata
    • Journal Title

      Taiwanese J. Math.

      Volume: 15

    • Related Report
      2011 Research-status Report
    • Peer Reviewed
  • [Journal Article] Real-linar isometries between function algebras.2011

    • Author(s)
      T. Miura
    • Journal Title

      Cent. Eur. J. Math.

      Volume: 9

    • Related Report
      2011 Research-status Report
    • Peer Reviewed
  • [Journal Article] Divisibly norm-preseving maps betwenn commutative Banach algebras.2011

    • Author(s)
      T. Miura, D. Honma and R. Shindo
    • Journal Title

      Rocky Mountain J. Math.

      Volume: 41

    • Related Report
      2011 Research-status Report
    • Peer Reviewed
  • [Journal Article] Spectral preserver problems in commutative Banach algebras.2011

    • Author(s)
      O. Hatori, S. Lambert, A. Luttman, T. Miura, T. Tonev and R. Yates
    • Journal Title

      Contemp. Math.

      Volume: 547

    • Related Report
      2011 Research-status Report
    • Peer Reviewed
  • [Journal Article] Spectral radii conditions for isomorphisms between unital semisimple commutative Banach algebras.2011

    • Author(s)
      G. Hirasawa T. Miura and H. Takagi
    • Journal Title

      Contemp. Math.

      Volume: 547

    • Related Report
      2011 Research-status Report
    • Peer Reviewed
  • [Presentation] 関数環上のスペクトル保存写像の拡張2015

    • Author(s)
      三浦 毅,Thomas Tonev
    • Organizer
      日本数学会
    • Place of Presentation
      明治大学(東京都・千代田区)
    • Year and Date
      2015-03-23
    • Related Report
      2014 Annual Research Report
  • [Presentation] 関数空間上の等距離写像とその例2015

    • Author(s)
      三浦 毅
    • Organizer
      つくばセミナー
    • Place of Presentation
      筑波大学(茨城県・つくば市)
    • Year and Date
      2015-03-06
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] 関数空間上の全射等距離写像2014

    • Author(s)
      三浦 毅
    • Organizer
      集合論的・幾何学的トポロジーと種々の分野の交流
    • Place of Presentation
      京都大学数理解析研究所(京都府・京都市)
    • Year and Date
      2014-10-23
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] Surjective isometries between function spaces2014

    • Author(s)
      Takeshi Miura
    • Organizer
      The Seventh Conference on Function Spaces
    • Place of Presentation
      Southern Illinois University at Edwardsville (Illinois, America)
    • Year and Date
      2014-05-22
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] Real linear isometries between function algebras2011

    • Author(s)
      T. Miura
    • Organizer
      Reaserch on preserver problems concerning to Banach algebras and its applications
    • Place of Presentation
      京都大学数理解析研究所
    • Related Report
      2011 Research-status Report
  • [Presentation] 関数環上の実線形等距離写像の構造2011

    • Author(s)
      三浦 毅
    • Organizer
      関数環研究集会
    • Place of Presentation
      山形大学
    • Related Report
      2011 Research-status Report
  • [Presentation] 関数環上の全射等距離写像

    • Author(s)
      三浦 毅
    • Organizer
      日本数学会
    • Place of Presentation
      愛媛大学
    • Related Report
      2013 Research-status Report
  • [Presentation] Isometries between function spaces

    • Author(s)
      H. Koshimizu, T. Miura, H. Takagi and S.-E. Takahasi
    • Organizer
      Complex Analysis and Applications '13
    • Place of Presentation
      The Institute of Mathematics and Informatics, Bulgaria
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] 関数環上のある種のスペクトル保存写像の構造,II

    • Author(s)
      三浦 毅
    • Organizer
      関数環研究集会
    • Place of Presentation
      クロスパルにいがた
    • Related Report
      2013 Research-status Report
  • [Presentation] Surjective Isometries between function spaces

    • Author(s)
      Takeshi Miura
    • Organizer
      Department of Mathematical Sciences, Colloquium Series
    • Place of Presentation
      The University of Montana
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] Surjective Isometries between function algebras

    • Author(s)
      Takeshi Miura
    • Organizer
      International Conference on Mathematics and Statictics
    • Place of Presentation
      University of Memphis
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] 関数環上のある種のスペクトル保存写像の構造

    • Author(s)
      三浦 毅
    • Organizer
      関数環研究集会
    • Place of Presentation
      日本大学
    • Related Report
      2012 Research-status Report
  • [Presentation] 関数空間上の全射等距離写像と端点の性質

    • Author(s)
      三浦 毅
    • Organizer
      つくばセミナー
    • Place of Presentation
      筑波大学
    • Related Report
      2012 Research-status Report

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Published: 2011-08-05   Modified: 2019-07-29  

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