2003 Fiscal Year Annual Research Report

可換Banach環上の環準同形写像の自己線形性の研究

Research Project

Project/Area Number	14540161
Research Institution	NIIGATA UNIVERSITY
Principal Investigator	羽鳥理新潟大学, 理学部, 教授 (70156363)
Co-Investigator(Kenkyū-buntansha)	渡辺恵一新潟大学, 理学部, 助教授 (50210894) 斎藤吉助新潟大学, 理学部, 教授 (30018949) 泉地敬司新潟大学, 理学部, 教授 (80120963) 三浦毅山形大学, 留学生センター, 助教授 (90333989) 高橋眞映山形大学, 工学部, 教授 (50007762)
Keywords	commutative Banach algebra / ring homomorphism / composition operator
Research Abstract	Banach環には3つの演算(和,スカラー倍,積)が定まっているのでBanach環上の写像を考えるにあたっては3つの演算を保存する写像(準同形写像)を考えるのが自然であるが,スカラー倍の保存を仮定しない環準同形写像が自動的に線形である場合が多い。環準同形写像が自動的に線形写像になるための条件を考察し,スペクトルが大きいような要素を含む可換Banach環上の環準同形写像は線形写像となることを示した。この結果により円板環上の環準同形写像はじめ多くの環準同形写像が線形写像(すなわち多元環としての準同形写像)であることがわかった。実可換Banach環から狭義の実可換Banach環への環準同形写像は,極大イデアル空間の間のある種の連続関数で記述できることを示した。また,互いに特異な測度に対して、その特異性が円板上の有界正則関数のBanach環の極大イデアル空間に表現できることを示した。また互いに特異な測度の特異性、および測度の絶対連続性が極大イデアル空間に表現できることを示し割算問題に応用した。極大イデアルの共通部分で表せるイデアルの十分条件を与えた。また1つの外部関数で生成される閉イデアルがそのようになるときの必要十分条件を与えた。また,複素ユークリッド空間上のabsoluteノルムがsmoothであるための特徴付けを与えた。楕円型微分方程式に関連するWirtinger型不等式,微分幾何に関連があるといわれるBeesackの不等式を統一的に論じた。特に,Banach空間に値を持つ関数まで拡張した。C(X)上の荷重合成作用素の本質的ノルム及びHyers-Ulam stability constantが,ある種の同じレベル集合の言葉で完全に記述した。

Research Products

(23 results)

All Other

All Publications (23 results)

[Publications] Osamu Hatori: "Characterizations and automatic linearity for ring homomorphisms on algebras of functions"Contemp.Math.. 328. 201-215 (2003)
[Publications] Keiji Izuchi: "K-hulls of QC-level sets"Indiana Univ.Math.. 52・2. 421-436 (2003)
[Publications] P.Gorkin: "Sequences separating fibers in the spectrum of H^∞"Topology Appl.. 129・3. 221-238 (2003)
[Publications] K.Izuchi: "Common zero sets of equivalent singular inner functions"Studia Math.. 発表予定.
[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.
[Publications] K.Izuchi: "Norm closed invariant spaces in L^∞ and H^∞"Glasgow Math.J.. 発表予定.
[Publications] K.Izuchi: "Backward shift invariant subspaces in the bidisc"Hokkaido Math.J.. 発表予定.
[Publications] K.Izuchi: "Backward shift invariant subspaces in the bidisc II"J.Operator Theory. 発表予定.
[Publications] K.Izuchi: "The structure of the maximal ideal space of H^∞"Sugaku Expositions. 発表予定.
[Publications] J.S.Choa: "A note on maximal inner spaces of the Bergman space"Integral Eq.Op.Th.. 発表予定.
[Publications] K.Izuchi: "Strictly contractive compression on backward shift invairant subspaces over the torus"Acta Sci.Math.(Szeged). 発表予定.
[Publications] Kichi-Suke Saito: "Uniform convexity of ψ-direct sums of Banach spaces"Journal of Mathematical Analysis and Applications. 277. 1-11 (2003)
[Publications] Mikio Kato: "On ψ-direct sums of Banach spaces and convexity"Journal of the Australian Mathematical Society. 75. 413-422 (2003)
[Publications] K.Mitani: "Smoothness of absolute norms on C^n"J.Convex Analysis. 10. 89-107 (2003)
[Publications] K.Mitani: "The James constant of absolute norms on R^2"Journal of Nonlinear and Convex Analysis. 4. 399-410 (2003)
[Publications] Mikio Kato: "Uniform non-squareness of ψ-direct sums of Banach spaces 【symmetry】ψY"Mathematical Inequalities and Applications. 発表予定.
[Publications] Takeshi Miura: "A characterization of Hyers-Ulam stability of first order linear Differential operators"J.Math.Anal.Appl.. 286. 136-146 (2003)
[Publications] Sin-Ei Takahasi: "On the structure of the solution set of a third kind boundary value problem"Math.Nachr.. 257. 99-107 (2003)
[Publications] Sin-Ei Takahasi: "A note on Wirtinger-Beesack's inequality"Math.Inequal.Appl.. 6・2. 277-282 (2003)
[Publications] Takeshi Miura: "Ring homomorphisms on real Banach algebras"Internat.J.Math.and Math.Sci.. 48. 3025-3029 (2003)
[Publications] Takuya Hara: "On weighted extensions of Garleman's inequality and Hardy's inequality"Math.Inequal.Appl.. 6・4. 667-674 (2003)
[Publications] Takeshi Miura: "Hyers-Ulam stability of linear differential operator with constant coefficients"Math.Nachr.. 258. 90-96 (2003)
[Publications] Hiroyuki Takagi: "Essential norm and stability constant of weighted composition operators on C(X)"Bull.Korean Math.Soc.. 40・4. 583-591 (2003)

2003 Fiscal Year Annual Research Report

可換Banach環上の環準同形写像の自己線形性の研究

Principal Investigator

羽鳥 理 新潟大学, 理学部, 教授 (70156363)

Research Products

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

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

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

[Publications] K.Izuchi: "Common zero sets of equivalent singular inner functions"Studia Math.. 発表予定.

[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.

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

[Publications] K.Izuchi: "Backward shift invariant subspaces in the bidisc"Hokkaido Math.J.. 発表予定.

[Publications] K.Izuchi: "Backward shift invariant subspaces in the bidisc II"J.Operator Theory. 発表予定.

[Publications] K.Izuchi: "The structure of the maximal ideal space of H^∞"Sugaku Expositions. 発表予定.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

羽鳥理新潟大学, 理学部, 教授 (70156363)