Equivalent metrics on normal composition operators

Mohammad R. Jabbarzadeh; Seddighe Haghighatjoo

doi:10.1216/rmj.2020.50.989

Abstract

We define some metrics on the set of all bounded normal composition operators in $L^{2} (Σ)$ , and show that these metrics are equivalent with the metric induced by the usual operator norm.

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Mohammad R. Jabbarzadeh. Seddighe Haghighatjoo. "Equivalent metrics on normal composition operators." Rocky Mountain J. Math. 50 (3) 989 - 999, June 2020. https://doi.org/10.1216/rmj.2020.50.989

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Received: 2 June 2019; Revised: 20 December 2019; Accepted: 27 December 2019; Published: June 2020

First available in Project Euclid: 29 July 2020

zbMATH: 07235592

MathSciNet: MR4132622

Digital Object Identifier: 10.1216/rmj.2020.50.989

Subjects:

Primary: 47A30

Secondary: 47B38

Keywords: Composition operators , gap metric , Moore–Penrose inverse , normal operator

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