Band projections in spaces of regular operators

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY Accounts of Chemical Research Pub Date : 2024-03-09 DOI:10.1090/tran/9162

David Muñoz-Lahoz, Pedro Tradacete

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Abstract

We introduce inner band projections in the space of regular operators on a Dedekind complete Banach lattice and study some structural properties of this class. In particular, we provide a new characterization of atomic order continuous Banach lattices as those for which all band projections in the corresponding space of regular operators are inner. We also characterize the multiplication operators L A R B L_AR_B which are band projections precisely as those with A , B A,B being band projections up to a scalar multiple.

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正则算子空间中的带投影

我们在戴德金完整巴拿赫网格上的正则算子空间中引入了内带投影，并研究了这一类的一些结构性质。特别是，我们提供了原子阶连续巴拿赫网格的一个新特征，即相应正则算子空间中的所有带投影都是内投影。我们还描述了带投影的乘法算子 L A R B L_AR_B 的特征，即 A , B A,B 是直到标量倍数的带投影。

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

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.

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