Study on Banach algebras from general and geometric topology view point

从一般和几何拓扑角度研究Banach代数

• 批准号: 18540066
• 负责人: KAWAMURA Kazuhiro
• 金额: $ 2.57万
• 依托单位: University of Tsukuba
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2006
• 资助国家: 日本
• 起止时间: 2006 至 2007
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-18540066/
• 关键词: Banach Algebra; Algebraic equation; Spectrum preserving map; dimension theory; mapping space; バナツハ環; スペクトル保存; スペクトル

The purpose of this research is to study algebra and geometry of Banach algebra by making use of general and geometric topology. Two workshops "Seminar on Banach algebras" were held by the support of the present grant (2006. 11. 15-16 & 2007, 11. 21 - 22 University of Tsukuba. On the basis of the discussion at the workshop, some progress was made on the characterization problem of algebraically closed algebras of continuous functions. K. Kawamura, with T. Miura, N. Brodskiy, J. Dydak and A. Karasev, obtained of continuous functions. K. Kawamura, with T. Miura, N. Brodskiy, J. Dydak and A. Karasev, obtained several results which demonstrate that the algebraic closedness strongly depends on the first-countability of the underlying space. T. Miura with D. Honma also investigate other types of equations on function algebras. O. Hatori, T. Miura with H. Oka, H. Takagi and S-E. Takahasi, investigated spectrum-preserving maps on semisimple unital Banach algebras and uniform algebras of analytic functions of two variables and obtained some conditions for these map to be isomorphisms or isometries. K. Sakai with S. Uehara, W. Kubis and K. Mine studied some hyperspaces and function spaces from the view point of infinite dimensional topological manifolds. One of the results states that the topological type of open subsets of LF space is determined by their homotopy types, a pioneering work on the theory of LF manifolds. H. Kato with E. Matsuhashi, C. Mouron investigated Bing maps and Krasinkewicz maps, the complete opposite to smooth maps yet generc, and hereditarily indecomposable continua in view of dimension theory and topological dynamics. K. Yamazaki studied extension problems of set-valued functions and gave a characterization of countable monotone paracompactness in terms of the extension property. K. Eda with V. Matijevic studied the covering homomorphism between two dimensional solenoids.

本文的目的是利用一般拓扑学和几何拓扑学研究Banach代数的代数和几何。两个研讨会“巴拿赫代数研讨会”举行的支持下，目前的赠款（2006年。11. 15-16和2007年，11。21 - 22筑波大学。在研讨会讨论的基础上，对连续函数代数闭代数的刻画问题取得了一些进展。K. Kawamura，T. Miura，N. Brodskiy，J. Dydak和A. Karasev，连续函数的获得。K. Kawamura，T. Miura，N. Brodskiy，J. Dydak和A. Karasev等人得到了几个结果，证明了代数闭性强烈依赖于底层空间的第一可数性。T. Miura与D.本间还研究了函数代数上的其他类型的方程。O.服部，T。Miura与H。Oka，H.高木和S-E。Takahasi等研究了二元解析函数的半单单位Banach代数和一致代数上的保谱映射，得到了这类映射是同构或等距的一些条件。K. Sakai与S。Uehara，W. Kubis和K.我从无穷维拓扑流形的角度研究了一些超空间和函数空间。其中一个结果指出LF空间的开子集的拓扑类型是由它们的同伦类型决定的，这是LF流形理论的一个开拓性工作。H. Kato与E.松桥角Bingon研究了Bing映射和Krasinkewicz映射，这两个映射与光滑映射完全相反，但又是一般的，并且根据维数理论和拓扑动力学研究了遗传不可分解的连续统。K. Yamazaki研究了集值函数的延拓问题，并利用延拓性质给出了可数单调仿紧性的一个刻画。K. Eda和V. Matijevic研究了二维空间的覆盖同态。

项目成果

HYERS-ULAM STABILITY OF A CLOSED OPERATOR IN A HILBERT SPACE

• DOI: 10.4134/bkms.2006.43.1.107
• 发表时间: 2006-02
• 期刊: Bulletin of The Korean Mathematical Society
• 影响因子: 0.5
• 作者: Go Hirasawa;T. Miura

On surjective ring homomorphisms between semi-simple commutative Banach algebras

半单交换Banach代数间的满射环同态

• 发表时间: 2008
• 期刊: Publ.Math.Debrecen 73
• 作者: Takeshi Miura;Sin-Ei Takahasi;Norio Niwa;Hirokazu Oka
• 通讯作者: Hirokazu Oka

A perturbation of normal operators on a Hilbert space

希尔伯特空间上正规算子的扰动

• 发表时间: 2008
• 期刊: Nonlinear Funct. Anal. Appl. 13
• 作者: Takeshi Miura;Sin-Ei Takahasi;Norio Niwa;Hirokazu Oka;Takeshi Miura
• 通讯作者: Takeshi Miura

A Cauchy-Euler type factorization of operators

算子的柯西-欧拉型分解

• 发表时间: 2008
• 期刊: Tokyo J. Math 31-2
• 作者: Takeshi Miura;Sin-Ei Takahasi;Norio Niwa;Hirokazu Oka;Takeshi Miura;Sin-Ei Takahasi
• 通讯作者: Sin-Ei Takahasi

Products of weak P-spaces and K-analytic spaces

弱 P 空间和 K 解析空间的乘积

• 发表时间: 2008
• 期刊: Mathematika (印刷中)
• 作者: V;Gutev・H;ohta ・K;Yamazaki;K. Sakai;H. Kato and C. Mouron;W Kubis and K. Sakai;K. Mine and K. Sakai;K. Yamazaki
• 通讯作者: K. Yamazaki