乘数和平均遍历乘法算子的最大模原理

IF 0.7 4区数学 Q2 MATHEMATICS

Journal of Operator Theory Pub Date : 2020-07-22 DOI:10.7900/jot.2020aug11.2299

E. Bilokopytov

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引用次数: 1

摘要

这个注记的主要目的是证明连通Hausdorff拓扑空间上连续函数的一类广义赋范空间的（不一定全纯的）乘子不能达到它们的乘子范数，除非它们是常数。作为一种应用，压缩乘法算子要么是与常数的乘积，要么是完全非酉的。此外，我们还探讨了乘法算子（弱）紧致和（一致）均值遍历的可能性。

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Maximum modulus principle for multipliers and mean ergodic multiplication operators

The main goal of this note is to show that (not necessarily holomorphic) multipliers of a wide class of normed spaces of continuous functions over a connected Hausdorff topological space cannot attain their multiplier norms, unless they are constants. As an application, a contractive multiplication operator is either a multiplication with a constant, or is completely non-unitary. Additionally, we explore possibilities for a multiplication operator to be (weakly) compact and (uniformly) mean ergodic.

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来源期刊

Journal of Operator Theory 数学-数学

CiteScore

1.30

自引率

12.50%

发文量

审稿时长

12 months

期刊介绍： The Journal of Operator Theory is rigorously peer reviewed and endevours to publish significant articles in all areas of operator theory, operator algebras and closely related domains.