正则算子空间中的带投影

IF 1.2 2区数学 Q1 MATHEMATICS

Transactions of the American Mathematical Society Pub Date : 2024-03-09 DOI:10.1090/tran/9162

David Muñoz-Lahoz, Pedro Tradacete

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引用次数: 0

摘要

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。

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Band projections in spaces of regular operators

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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来源期刊

Transactions of the American Mathematical Society 数学-数学

CiteScore

2.30

自引率

7.70%

发文量

171

审稿时长

3-6 weeks

期刊介绍： All articles submitted to this journal are peer-reviewed. The AMS has a single blind peer-review process in which the reviewers know who the authors of the manuscript are, but the authors do not have access to the information on who the peer reviewers are. This journal is devoted to research articles in all areas of pure and applied mathematics. To be published in the Transactions, a paper must be correct, new, and significant. Further, it must be well written and of interest to a substantial number of mathematicians. Piecemeal results, such as an inconclusive step toward an unproved major theorem or a minor variation on a known result, are in general not acceptable for publication. Papers of less than 15 printed pages that meet the above criteria should be submitted to the Proceedings of the American Mathematical Society. Published pages are the same size as those generated in the style files provided for AMS-LaTeX.