A Banach space theoretical characterization of abelian 𝐶*-algebras

Proceedings of the American Mathematical Society, Series B Pub Date : 2023-06-07 DOI:10.1090/bproc/175

Ryotaro Tanaka

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引用次数: 1

Abstract

A Banach space theoretical characterization of abelian C ∗ C^* - algebras among all C ∗ C^* -algebras is given. As an application, it is shown that if A A and B B are C ∗ C^* -algebras (nonlinearly) isomorphic to each other with respect to the structure of Birkhoff-James orthogonality, and if either A A or B B is abelian, then they are ∗ * -isomorphic. Moreover, it is pointed out that the same kind of characterization is not valid for preduals of abelian von Neumann algebras.

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abelian *代数的Banach空间理论表征

给出了所有C * C^* -代数中阿贝尔C * C^* -代数的一个巴拿赫空间理论刻划。作为一个应用，证明了如果A A和B B在Birkhoff-James正交结构上是C * C^* -代数(非线性)同构，且A A或B B是阿贝的，则它们是* * -同构。此外，本文还指出，对于阿贝尔-冯-诺伊曼代数的前偶，同样的性质是不成立的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Proceedings of the American Mathematical Society, Series B

CiteScore

1.60

自引率

0.00%

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