Anti-C*-algebras

IF 1.1 2区数学 Q1 MATHEMATICS

Banach Journal of Mathematical Analysis Pub Date : 2024-08-07 DOI:10.1007/s43037-024-00367-5

Robert Pluta, Bernard Russo

引用次数: 0

Abstract

We introduce a class of Banach algebras that we call anti-C*-algebras. We show that the normed standard embedding of a C*-ternary ring is the direct sum of a C*-algebra and an anti-C*-algebra. We prove that C*-ternary rings and anti-C*-algebras are semisimple. We give two new characterizations of C*-ternary rings which are isomorphic to a TRO (ternary ring of operators), providing answers to a query raised by Zettl (Adv Math 48(2): 117–143, 1983), and we propose some problems for further study.

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反 C* 结构

我们引入一类巴拿赫代数，称之为反 C* 代数。我们证明了 C* 三元环的规范标准嵌入是 C* 代数和反 C* 代数的直接和。我们证明了 C* 三元环和反 C* 代数是半简单的。我们给出了与 TRO（三元运算环）同构的 C*-ternary 环的两个新特征，解答了 Zettl 提出的一个问题（Adv Math 48(2)：117-143, 1983）提出的疑问提供了答案，我们还提出了一些有待进一步研究的问题。

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

Banach Journal of Mathematical Analysis 数学-数学

CiteScore

2.00

自引率

8.30%

发文量

审稿时长

>12 weeks

期刊介绍： The Banach Journal of Mathematical Analysis (Banach J. Math. Anal.) is published by Birkhäuser on behalf of the Tusi Mathematical Research Group. Banach J. Math. Anal. is a peer-reviewed electronic journal publishing papers of high standards with deep results, new ideas, profound impact, and significant implications in all areas of functional analysis and operator theory and all modern related topics. Banach J. Math. Anal. normally publishes survey articles and original research papers numbering 15 pages or more in the journal’s style. Shorter papers may be submitted to the Annals of Functional Analysis or Advances in Operator Theory.