Isolation amongst composition operators on $L^p(\mu)$-spaces $(1\le p \le \infty)$

IF 0.6 4区数学 Q3 MATHEMATICS Operators and Matrices Pub Date : 2023-01-01 DOI:10.7153/oam-2023-17-13

Ashish Naudiyal, H. Chandra

引用次数: 0

Abstract

. In this paper we show that each composition operator is isolated in comp ( L p ) ( 1 (cid:2) p (cid:2) ∞ ) under the norm topology. We also prove that while each composition operator is non-isolated in comp ( (cid:2) p ) ( 1 (cid:2) p < ∞ ) under the strong operator topology, every composition operator is isolated in comp ( L ∞ ) under the strong operator topology.

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$L^p(\mu)$ -空间上组合运算符之间的隔离 $(1\le p \le \infty)$

．本文证明了在范数拓扑下，每个复合算子在comp (L p) (1 (cid:2) p (cid:2)∞)上是孤立的。我们还证明了在强算子拓扑下，每个复合算子在comp ((cid:2) p) (1 (cid:2) p <∞)上是不孤立的，而在强算子拓扑下，每个复合算子在comp (L∞)上是孤立的。

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

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.

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