性质(gt)在摄动和张量积作用下的稳定性

IF 0.6 4区数学 Q3 MATHEMATICS

Operators and Matrices Pub Date : 2023-01-01 DOI:10.7153/oam-2023-17-19

M. Rashid, M. Chō

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引用次数: 0

摘要

．作用于巴拿赫空间X上的算子T符合性质(gt)，如果T的谱的独立性点(T)的特征值恰好是谱上的点(T - T)，其中T是索引小于等于0的上半b -Fredholm。本文研究了性质(gt)在有限秩算子、幂零算子以及与T交换的代数算子摄动下的稳定性。此外，我们研究了作用于Banach空间X上的有界线性算子T和作用于Banach空间Y上的有界线性算子S到它们的张量积T⊗S的性质(gt)的转移。数学

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The stability of property (gt) under perturbation and tensor product

. An operator T acting on a Banach space X obeys property ( gt ) if the isolated points of the spectrum  ( T ) of T which are eigenvalues are exactly those points  of the spectrum for which T −  is an upper semi-B -Fredholm with index less than or equal to 0. In this paper we study the stability of property ( gt ) under perturbations by ﬁ nite rank operators, by nilpotent operators and, more generally, by algebraic operators commuting with T . Moreover, we study the transfer of property ( gt ) from a bounded linear operator T acting on a Banach space X and a bounded linear operator S acting on a Banach space Y to their tensor product T ⊗ S . Mathematics

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来源期刊

Operators and Matrices 数学-数学

CiteScore

0.90

自引率

0.00%

发文量

审稿时长

7 months

期刊介绍： ''Operators and Matrices'' (''OaM'') aims towards developing a high standard international journal which will publish top quality research and expository papers in matrix and operator theory and their applications. The journal will publish mainly pure mathematics, but occasionally papers of a more applied nature could be accepted. ''OaM'' will also publish relevant book reviews. ''OaM'' is published quarterly, in March, June, September and December.