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

Pub Date : 2023-01-01 DOI:10.7153/oam-2023-17-13

Ashish Naudiyal, H. Chandra

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引用次数: 0

摘要

．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。

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

. 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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