Certain spectra preserving maps on Banach algebras and the stability of their perturbations

• Project/Area Number: 19740063
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Single-year Grants
• Research Field: Basic analysis
• Research Institution: Yamagata University
• Principal Investigator: MIURA Takeshi 山形大学, 大学院・理工学研究科, 教授 (90333989)
• Project Period (FY): 2007 – 2010
• Project Status: Completed (Fiscal Year 2010)
• Budget Amount: ¥3,400,000 (Direct Cost: ¥2,800,000、Indirect Cost: ¥600,000); Fiscal Year 2010: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000); Fiscal Year 2009: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2008: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2007: ¥800,000 (Direct Cost: ¥800,000)
• Keywords: 関数解析学 / Banach環 / スペクトル保存 / 摂動と安定性 / スペクトル保存写像

Research Abstract

Molnar investigated, what is so called "multiplicatively spectra preserving maps" between C^*-algebras, and characterized such maps. We generalized the result by Molnar to such maps between unital, semisimple commutative Banach algebras. In addition, we proved that quite similar results to the above hold for "peripherally multiplicative maps" and "spectra radii preserving maps". We also investigated some differential equations in Banach space-valued function spaces, and gave a sufficient condition in order that Hyers-Ulam or Ger type stability hold.

Research Products

• [Journal Article] Additively spectral-radius preserving suejections between unital semisimple commutative Banach algebras (2010)
  • Author(s): O. Hatori, G. Hirasawa and T. Miura
  • Journal Title: Cent. Eur. J. Math. Volume: 8 Pages: 597-60
• [Journal Article] Generalizations of spectrally multiplicative surjections between uniform algebras (2010)
  • Author(s): O. Hatori, T. Miura, R. Shindo and H. Takagi
  • Journal Title: Rend. Circ. Mat. Palermo Volume: 59 Pages: 161-183
• [Journal Article] A generalization of the Banach-Stone theorem for commutative Banach algebras (2010)
  • Author(s): G. Hirasawa, T. Miura and R. Shindo
  • Journal Title: Nihonkai Math. J. Volume: 21 Pages: 1-10
• [Journal Article] Generalizations of spectrally multiplicative surjections between uniform algebras (2010)
  • Author(s): O.Hatori, T.Miura, R.Shindo, H.Takagi
  • Journal Title: Rend.Circ.Mat.Palermo (2) Volume: 59 Pages: 161-183
  • Peer Reviewed
• [Journal Article] Additively spectral-radius preserving surjections between unital semisimple commutative Banach algebras (2010)
  • Author(s): O.Hatori, G.Hirasawa, T.Miura
  • Journal Title: Cent.Eur.J.Math. Volume: 8 Pages: 597-601
  • Peer Reviewed
• [Journal Article] Approximate unitaries in B(H) (2010)
  • Author(s): M.Mirzavaziri, T.Miura, M.S.Moslehian
  • Journal Title: East.J.Approx. Volume: 16 Pages: 147-151
  • Peer Reviewed
• [Journal Article] On a Hyers-Ulam-Aoki-Rassias type stability and a fixed point theorem (2010)
  • Author(s): S.-E.Takahasi, T.Miura, H.Takagi
  • Journal Title: J.Nonlinear Convex Anal. Volume: 11 Pages: 423-439
  • Peer Reviewed
• [Journal Article] An equality condition of Arhippainen-Muller'sestimate and its related problem (2010)
  • Author(s): S.-E.Takahasi, T.Miura, T.Hayata
  • Journal Title: Taiwanese J.Math. Volume: 15 Pages: 165-169
  • Peer Reviewed
• [Journal Article] Peripherally monomial-preserving maps between uniform algebras (2009)
  • Author(s): O. Hatori, K. Hino, T. Miura and H. Oka
  • Journal Title: Meditter. J. Math. Volume: 6 Pages: 47-60
• [Journal Article] Stability of almost multiplicative functionals (2009)
  • Author(s): N. Niwa, H. Oka, T. Miura and S.-E. Takahasi
  • Journal Title: Aust. J. Math. Anal. Appl. Volume: 9 Pages: 47-60
• [Journal Article] Peripheral multiplicativity of maps on uniformly closed algebras of continuous functions which vanish at infinity (2009)
  • Author(s): O. Hatori, T. Miura, H. Oka and H. Takagi
  • Journal Title: Tokyo J. Math. Volume: 32 Pages: 91-104
• [Journal Article] An estimate of the commutativity of C^2-function and probability measure (2009)
  • Author(s): T. Miura, T. Hayata and S.-E. Takahasi
  • Journal Title: J. Math. Inequal. Volume: 3 Pages: 169-180
• [Journal Article] Superstability of generalized multiplicative functionals (2009)
  • Author(s): T. Miura, H. Takagi, M. Tsukada and S.-E. Takahasi
  • Journal Title: J. Inequal. Appl. Pages: 7-7
• [Journal Article] A generalization of peripherally multiplicative surjections between standard operator algebras (2009)
  • Author(s): T. Miura and D. Honma
  • Journal Title: Cent. Eur. J. Math. Volume: 7 Pages: 479-486
• [Journal Article] Ger type stability of the first order linear differential equation for holomorphic functions (2009)
  • Author(s): T. Miura
  • Journal Title: Nonlinear Funct. Anal. Appl. Volume: 14 Pages: 707-714
• [Journal Article] Peripherally monomial-preserving maps between uniform algebras (2009)
  • Author(s): Osamu Hatori, Kazumi Hino, Takeshi Miura, Hirokazu Oka
  • Journal Title: Mediterr. J. Math. 6 Pages: 47-60
  • Peer Reviewed
• [Journal Article] A generalization of peripherallymultiplicative surjections between standard operator algebras (2009)
  • Author(s): Takeshi Miura, Dai Honma
  • Journal Title: Cent. Eur. J. Math. 7 Pages: 479-486
  • Peer Reviewed
• [Journal Article] On the root closedness of continuous function algebras (2009)
  • Author(s): K.Kawamura, T.Miura
  • Journal Title: Topology Appl. 156 Pages: 624-628
  • Peer Reviewed
• [Journal Article] Peripherally monomial-preserving maps between uniform algebras (2009)
  • Author(s): O.Hatori, K.Hino, T.Miura, H.Oka
  • Journal Title: Mediterr.J.Math. 6 Pages: 47-60
  • Peer Reviewed
• [Journal Article] Stability of almost multiplicative functionals (2009)
  • Author(s): N.Niwa, H.Oka, T.Miura, S.-E.Takahasi
  • Journal Title: Aust.J.Math.Anal.Appl. 9 Pages: 1-8
  • Peer Reviewed
• [Journal Article] Peripheral multiplicativity of maps on uniformly closed algebras of continuous functions which vanish at infinity (2009)
  • Author(s): O.Hatori, T.Miura, H.Oka, H.Takagi
  • Journal Title: Tokyo J.Math. 32 Pages: 91-104
  • Peer Reviewed
• [Journal Article] An estimate of the commutativity of C^2-functions and probability measure (2009)
  • Author(s): T.Miura, T.Hayata, S.-E.Takahasi
  • Journal Title: J.Math.Inequal. 3 Pages: 169-180
  • Peer Reviewed
• [Journal Article] Superstability of generalized multiplicative functionals (2009)
  • Author(s): T.Miura, H.Takagi, M.Tsukada, S.-E.Takahasi
  • Journal Title: J.Inequal.Appl. Pages: 1-7
  • Peer Reviewed
• [Journal Article] A generalization of peripherally-multiplicative surjections between standard operator algebras (2009)
  • Author(s): T.Miura, D.Honma
  • Journal Title: Cent.Eur.J.Math. 7 Pages: 479-486
  • Peer Reviewed
• [Journal Article] Ger type stability of the first order linear differential equation y'(t)=h(t)y(t) (2008)
  • Author(s): T. Miura, H. Oka, S.-E. Takahasi and N. Niwa
  • Journal Title: Tamsui Oxf. J. Math. Sci. Volume: 24 Pages: 445-456
• [Journal Article] Ring homomorphisms on commutative regular Banach algebras (2008)
  • Author(s): T. Miura, S.-E. Takahasi and N. Niwa
  • Journal Title: Nihonkai Math. J. 19 Pages: 61-74
  • NAID: 110007605515
  • Peer Reviewed
• [Journal Article] On surjjective ring homomorphisms between semi-simple commutative Banach algebras (2008)
  • Author(s): T. Miura, S.-E. Takahasi, N. Niwa and H. Oka
  • Journal Title: Publ. Math. Debrecen 73 Pages: 119-131
  • Peer Reviewed
• [Journal Article] A perturbation of normal operators on a Hilbert space (2008)
  • Author(s): T. Miura, A. Uchiyama, H. Oka, G. Hirasawa, S.-E. Takahasi and N. Niwa
  • Journal Title: Nonlinear Funct. Anal 13 Pages: 291-297
  • Peer Reviewed
• [Journal Article] A Cauchy-Euler type factorization of operators (2008)
  • Author(s): S.-E. Takahasi, H. Oka, T. Miura and H. Takagi
  • Journal Title: Tokyo J. Math. 31 Pages: 489-493
  • Peer Reviewed
• [Journal Article] Ger type stability of the first order linear differential equation y'(t)=h(t)y(t) (2008)
  • Author(s): T. Miura, H. Oka, S.-E. Takahasi and N. Niwa
  • Journal Title: Tamsui Oxf. J. Math. Sci. 24 Pages: 445-456
  • Peer Reviewed
• [Journal Article] On the existence of continuous (approximate) roots of algebraic equations (2007)
  • Author(s): K. Kawamura and T. Miura
  • Journal Title: Topology Appl. Volume: 154 Pages: 434-442
• [Journal Article] Prime ideals and complex ring homomorphisms on a commutative algebra (2007)
  • Author(s): T. Miura, S.-E. Takahasi and N. Niwa
  • Journal Title: Publ. Math. Debrecen Volume: 70 Pages: 453-460
• [Journal Article] Exponential type functional equation and its Hyers-Ulam stability (2007)
  • Author(s): S.-E. Takahasi, T. Miura and H. Takagi
  • Journal Title: J. Math. Anal. Appl. Volume: 329 Pages: 1191-1203
• [Journal Article] Spectra preserving maps between commutative Banach algebras (2007)
  • Author(s): Osamu Hatori, Takeshi Miura, Hiroyuki Takagi
  • Journal Title: J. Math. Anal. Appl. 326 Pages: 281-296
  • Peer Reviewed
• [Journal Article] On the existence of continuous(approximate)roots of algebraic equations (2007)
  • Author(s): Kazuhiro, Kawamura, Takeshi, Miura
  • Journal Title: Topology. Appl. 154 Pages: 434-442
  • Peer Reviewed
• [Journal Article] Prime ideals and complex ring homomorphisms on a commutative Algebra (2007)
  • Author(s): Takeshi, Miura, Sin-Ei Takahasi, Norio, Niwa
  • Journal Title: Publ. Math. Debrecen 70 Pages: 453-460
  • Peer Reviewed
• [Journal Article] Exponential type functional equation and its Hyers-Ulam stability (2007)
  • Author(s): Sin-Ei, Takahasi, Takeshi, Miura, Hiroyuki, Takagi
  • Journal Title: J. Math. Anal. Appl. 329 Pages: 1191-1203
  • Peer Reviewed
• [Journal Article] On Wirtinger's inequality and its elementary proof (2007)
  • Author(s): Sin-Ei, Takahasi, Takeshi, Miura, Takahiro, Hayata
  • Journal Title: Math. Inequal. Appl. 10 Pages: 311-319
  • Peer Reviewed
• [Journal Article] A survey of certain algebraic equations in commutative C*-algebras (2007)
  • Author(s): Takeshi, Miura, Dai, Honma
  • Journal Title: Contemp. Math. 435 Pages: 327-333
  • Peer Reviewed
• [Journal Article] 2-local isometries and 2-local automorphisms on uniform algebras (2007)
  • Author(s): Osamu, Hatori, Takeshi, Miura, Hirokazu, Oka, Hiroyuki, Takagi
  • Journal Title: Int. Math. Forum 2 Pages: 2491-2502
  • Peer Reviewed
• [Journal Article] On a characterization of compact Hausdorff space X for which certain Algebraic equations are solvable in C(X) (2007)
  • Author(s): Dai, Honma, Takeshi, Miura
  • Journal Title: Tokyo J.Math. 30 Pages: 403-416
  • Peer Reviewed
• [Journal Article] Spectra preserving maps between commutative Banach algebras (2007)
  • Author(s): Osamu, Hatori, Takeshi, Miura, Hiroyuki, Takagi
  • Journal Title: J.Math.Anal.Appl. 326 Pages: 281-296
  • Peer Reviewed
• [Journal Article] An example of multiplicatively spectrum-preserving maps somorphic semi-simple commutative Banach algebras (2007)
  • Author(s): Osamu, Hatori, Takeshi, Miura, Hirokazu, Oka
  • Journal Title: Nihonkai Math.J. 18 Pages: 11-15
  • Peer Reviewed
• [Journal Article] Hyers-Ulam stability of the first order linear differential equations on Banach space-valued holomorphic mappings (2007)
  • Author(s): Takeshi, Miura, Hirokazu, Oka, Sin-Ei, Takahasi, Norio, Niwa
  • Journal Title: J.Math.Inequal. 1 Pages: 377-385
  • Peer Reviewed
• [Journal Article] Superstability of multipliers and ring derivations on Banach algebras (2007)
  • Author(s): Takeshi, Miura, Hirokazu, Oka, Go, Hirasawa, Sin-Ei, Takahasi
  • Journal Title: Banach J.Math.Anal. 1 Pages: 125-130
  • Peer Reviewed
• [Journal Article] Remarks on n-th root closedness for commutative C*-algebras (2007)
  • Author(s): Dai, Honma, Takeshi, Miura
  • Journal Title: Nihonkai Math.J. 18 Pages: 51-55
  • NAID: 110006665566
  • Peer Reviewed
• [Presentation] Function algebras上のisometries (2011)
  • Author(s): 三浦毅
  • Organizer: つくばセミナー
  • Place of Presentation: 筑波大学
  • Year and Date: 2011-03-07
• [Presentation] Function spaces上のisometries (2011)
  • Author(s): 古清水大直, 高木啓行, 三浦毅
  • Organizer: つくばセミナー
  • Place of Presentation: 筑波大学
  • Year and Date: 2011-03-07
• [Presentation] 関数環上の全射等距離写像 (2010)
  • Author(s): 三浦毅
  • Organizer: 関数環研究集会
  • Place of Presentation: 信州大学
  • Year and Date: 2010-11-30
• [Presentation] Banach-Stoneの定理とその拡張 (2010)
  • Author(s): 三浦毅
  • Organizer: 可換Banach環と種々の分野との交流II
  • Place of Presentation: 山形大学
  • Year and Date: 2010-06-27
• [Presentation] Generalizations of spectrally multiplicative surjections between uniform algebras (2010)
  • Author(s): T. Miura
  • Organizer: Function Spaces
  • Place of Presentation: Southern Illinois University at Edwardsville (Missouri)
  • Year and Date: 2010-05-18
• [Presentation] Generalizations of spectrally multiplicative surjections between uniform algebras (2010)
  • Author(s): T.Miura
  • Organizer: The Sixth Conference of Function Spaces
  • Place of Presentation: Southern Illinois University at Edwardsville(招待講演)
  • Year and Date: 2010-05-18
• [Presentation] 乗法的複素数値関数を超安定にさせる2項演算の決定 (2010)
  • Author(s): 高橋眞映, 三浦毅, 高木啓行
  • Organizer: 日本数学会
  • Place of Presentation: 慶応義塾大学
  • Year and Date: 2010-03-26
• [Presentation] Standard operator algebra 上の peripheral spectrum 保存写像2 (2009)
  • Author(s): 三浦毅
  • Organizer: 関数環研究集会
  • Place of Presentation: 日本大学
  • Year and Date: 2009-11-27
• [Presentation] Volterra 型積分作用素の安定性 (2009)
  • Author(s): 三浦毅
  • Organizer: 局所コホモロジー加群およびその周辺09
  • Place of Presentation: 奈良教育大学
  • Year and Date: 2009-09-28
• [Presentation] 複素数値関数の超安定性と2項演算 (2009)
  • Author(s): 高橋眞映, 三浦毅, 塚田真, 高木啓行
  • Organizer: 日本数学会
  • Place of Presentation: 大阪大学
  • Year and Date: 2009-09-25
• [Presentation] Peripherally multiplicative surjections between uniform algebras, Special Session on Banach Algebras (2009)
  • Author(s): Takeshi Miura
  • Organizer: Topological Algebras, and Abstract Harmonic Analysis of the American Mathematical Society sectional meeting
  • Place of Presentation: San Francisco State University
  • Year and Date: 2009-04-26
• [Presentation] Peripherally multiplicative surjections between uniform algebras (2009)
  • Author(s): 三浦毅
  • Organizer: American Mathematical Society
  • Place of Presentation: San Francisco State University
  • Year and Date: 2009-04-26
• [Presentation] ある種のスペクトルを保存する可換Banach環上の写像 (2008)
  • Author(s): 三浦毅
  • Organizer: 実解析学シンポジウム
  • Place of Presentation: 山口大学
  • Year and Date: 2008-11-07
• [Presentation] A note on the stability of Volterra type integral equation (2008)
  • Author(s): Takeshi Miura
  • Organizer: The Twelfth International Conferece on Functional Equations and Inequalities
  • Place of Presentation: Poland, Bedlewo
  • Year and Date: 2008-09-08
• [Presentation] A note on the stability of Volterra type integral equation (2008)
  • Author(s): T. Miura
  • Organizer: The 12^<th> International Conference of Functional Equations and Inequalities
  • Place of Presentation: Poland, Bedlewo
  • Year and Date: 2008-09-08
• [Presentation] Banach環上のunitization上のnormに関する話 (2007)
  • Author(s): 高橋眞映・三浦毅
  • Organizer: 実解析学シンポジウム
  • Place of Presentation: 大阪教育大学
  • Year and Date: 2007-10-21
• [Presentation] 可換C*-環上の代数方程式について (2007)
  • Author(s): 本間大・三浦毅
  • Organizer: 日本数学会
  • Place of Presentation: 東北大学
  • Year and Date: 2007-09-22
• [Presentation] 関数環上のある種の値域保存写像 (2007)
  • Author(s): 羽鳥理, 三浦毅, 高木啓行
  • Organizer: 日本数学会
  • Place of Presentation: 東北大学(宮城県仙台市)
  • Year and Date: 2007-09-21
• [Presentation] 作用素のCauchy-Euler型因数分解 (2007)
  • Author(s): 高橋眞映・岡裕和・三浦毅・高木啓行
  • Organizer: 日本数学会
  • Place of Presentation: 東京大学
  • Year and Date: 2007-09-21
• [Presentation] 関数環上のある種の値域保存写像 (2007)
  • Author(s): 羽烏理・三浦毅・高木啓行
  • Organizer: 日本数学会
  • Place of Presentation: 東北大学
  • Year and Date: 2007-09-21
• [Presentation] 可換C*-環に係数をもつある種の代数方程式の可解性と極大イデアル空間の位相構造 (2007)
  • Author(s): 三浦毅
  • Organizer: 実函数論・函数解析学合同シンポジウム
  • Place of Presentation: 九州大学
  • Year and Date: 2007-08-08