算子元组的射影联合谱与约简子空间

IF 1 3区数学 Q1 MATHEMATICS

Annals of Functional Analysis Pub Date : 2025-03-13 DOI:10.1007/s43034-025-00417-5

Michael I. Stessin

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引用次数: 0

摘要

如果一个有界算子元组有一个有限维的公共约简子空间，则它的射影联合谱有一个代数分量。一般情况下，反命题是不成立的，在射影联合谱中可能存在没有相应的公共约简子空间的代数分量。本文给出了这种对应发生的充分必要条件。

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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Projective joint spectra and reducing subspace of operator tuples

If a tuple of bounded operators have a common reducing subspace of finite dimension, its projective joint spectrum has an algebraic component. In general, the converse is not true and there might be algebraic components in the projective joint spectrum without corresponding common reducing subspaces. In this paper, we give necessary and sufficient conditions for the occurrence of such correspondence.

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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.