The Toeplitzness of weighted composition operators on Banach spaces of holomorphic functions
The Toeplitzness of weighted composition operators on Banach spaces of holomorphic functions
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DOI：
10.1080/17476933.2023.2196417
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发表时间：
2023-04
影响因子：
0.9
通讯作者：
M. Lindström;S. Miihkinen;P. Mleczko;D. Norrbo
中科院分区：
文献类型：
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作者：
M. Lindström;S. Miihkinen;P. Mleczko;D. Norrbo
各种渐近Toeplitz算子的概念最初是在Hardy-Hilbert空间中定义和研究的。本文的目的是将这些定义推广到全纯函数的Banach空间，包括哈代空间，Hardy-Lorentz空间和Hardy-Orlicz空间。给出了加权复合算子的一致渐近Toeplitz性和平均弱渐近Toeplitz性的函数论刻画。我们还研究了加权复合算子的强渐近Toeplitz性和弱渐近Toeplitz性。
ABSTRACT The concepts of various kinds of asymptotically Toeplitz operators have been originally defined and studied for the Hardy–Hilbert space. The aim of this article is to extend these definitions to the case of operators acting on Banach spaces of holomorphic functions, including Hardy spaces, Hardy–Lorentz spaces, and Hardy–Orlicz spaces. We give a function-theoretic characterization of uniformly asymptotically Toeplitzness and mean weakly asymptotically Toeplitzness for weighted composition operators. We also investigate strong and weak asymptotic Toeplitzness of weighted composition operators.