关于 Bochner-Schoenberg-Eberlein 和 Bochner-Schoenberg-Eberlein 模块性质的简单证明

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-05-02 DOI:10.1155/2024/5893357

Shirin Tavkoli, Rasoul Abazari, Ali Jabbari

引用次数: 0

摘要

让是一个非空集，是一个交换巴拿赫代数，并且是.在本文中，我们对有关.的 BSE（巴拿赫空间扩展）性质的结果提出了一个简明的证明。具体地说，我们确定，当且仅当是有限的并且是 BSE 时，.具有 BSE 性质。此外，我们还研究了巴拿赫模块的 BSE 模块性质，并证明当且仅当是有限的且代表一个 BSE 巴拿赫模块时，巴拿赫空间才是一个 BSE 巴拿赫模块。

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Simple Proofs for Bochner-Schoenberg-Eberlein and the Bochner-Schoenberg-Eberlein Module Properties on

Let be a nonempty set, be a commutative Banach algebra, and . In this paper, we present a concise proof for the result concerning the BSE (Banach space extension) property of . Specifically, we establish that possesses the BSE property if and only if is finite and is BSE. Additionally, we investigate the BSE module property on Banach -modules and demonstrate that a Banach space serves as a BSE Banach -module if and only if is finite and represents a BSE Banach -module.

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.