Some Characterizations for Composition Operators on the Fock Space
Liangying Jiang, Gabriel T. Prajitura, Ruhan Zhao
TL;DR
This paper thoroughly characterizes composition operators on Fock spaces, analyzing properties like essential norm, normality, spectra, cyclicity, and Schatten class membership, providing comprehensive criteria and comparisons with Hardy and Bergman spaces.
Contribution
It offers new, detailed characterizations of composition operators on Fock spaces for various properties, filling gaps in the existing literature.
Findings
Complete characterizations of essential norm and spectra.
Criteria for normality, cyclicity, and Schatten class membership.
Comparative analysis with Hardy and Bergman space operators.
Abstract
We study composition operators on the Fock spaces , problems considered include the essential norm, normality, spectra, cyclicity and membership in the Schatten classes. We give perfect answers for these basic properties, which present lots of different characterizations with the composition operators on the Hardy space or the weighted Bergman spaces.
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Taxonomy
TopicsHolomorphic and Operator Theory · Algebraic and Geometric Analysis · Advanced Topics in Algebra