Compact and Hilbert–Schmidt Differences of Weighted Composition Operators

Document Type

Article

Publication Date

1-1-2017

Publication Title

Integral Equations and Operator Theory

Volume

88

Issue

4

First page number:

465

Last page number:

482

Abstract

In this paper, we first obtain a characterization of compact difference of two weighted composition operators acting between the standard weighted Bergman spaces, under certain restrictions on the weights. We also calculate (upto equivalence) the Hilbert–Schmidt norm of a difference of two weighted composition operators acting from a Bergman space or Hardy space to an L2(μ) space. This result is followed by a few corollaries involving certain particular types of weights. We also investigate conditions for two weighted composition operators to lie on the same path component under the Hilbert–Schmidt norm topology. © 2017, Springer International Publishing.

Language

english

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