Isometric automorphisms of some reflexive algebras

IF 1.2 3区数学 Q1 MATHEMATICS

Annals of Functional Analysis Pub Date : 2025-01-09 DOI:10.1007/s43034-024-00400-6

Zhujun Yang, Hongjie Chen

引用次数: 0

Abstract

We construct a class of subspace lattices \({\mathcal {L}}\) on a separable infinite dimensional Hilbert space \(\mathcal {K}\). Let \({{\,\textrm{Alg}\,}}{\mathcal {L}}\) be the corresponding subspace lattice algebras. We show that every isometric automorphism of \({{\,\textrm{Alg}\,}}{\mathcal {L}}\) is spatial. We also show that \({{\,\textrm{Alg}\,}}{\mathcal {L}}\) are decomposable, and an operator in \({{\,\textrm{Alg}\,}}{\mathcal {L}}\) is single if and only if it is rank 1 under certain conditions.

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一些自反代数的等距自同构

在可分离无限维希尔伯特空间\(\mathcal {K}\)上构造了一类子空间格\({\mathcal {L}}\)。设\({{\,\textrm{Alg}\,}}{\mathcal {L}}\)为对应的子空间格代数。我们证明了\({{\,\textrm{Alg}\,}}{\mathcal {L}}\)的每一个等距自同构都是空间的。我们还证明了\({{\,\textrm{Alg}\,}}{\mathcal {L}}\)是可分解的，并且\({{\,\textrm{Alg}\,}}{\mathcal {L}}\)中的一个操作符是单个的，当且仅当它在某些条件下是排名1。

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

Annals of Functional Analysis MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.00

自引率

10.00%

发文量

期刊介绍： Annals of Functional Analysis is published by Birkhäuser on behalf of the Tusi Mathematical Research Group. Ann. Funct. 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 all modern related topics (e.g., operator theory). Ann. Funct. Anal. normally publishes original research papers numbering 18 or fewer pages in the journal’s style. Longer papers may be submitted to the Banach Journal of Mathematical Analysis or Advances in Operator Theory. Ann. Funct. Anal. presents the best paper award yearly. The award in the year n is given to the best paper published in the years n-1 and n-2. The referee committee consists of selected editors of the journal.