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2021 | OriginalPaper | Chapter

Is Every Nontrivial Hausdorff Operator on Lebesgue Space a Non-Riesz Operator?

Author : A. R. Mirotin

Published in: Operator Theory and Harmonic Analysis

Publisher: Springer International Publishing

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Abstract

We consider a generalization of Hausdorff operators on Lebesgue spaces and under natural conditions prove that such an operator is not a Riesz operator provided it is non-zero. In particular, it cannot be represented as a sum of a quasinilpotent and compact operators.

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Title: Is Every Nontrivial Hausdorff Operator on Lebesgue Space a Non-Riesz Operator?
Author: A. R. Mirotin
Publisher: Springer International Publishing
Book: Operator Theory and Harmonic Analysis
Print ISBN: 978-3-030-77492-9

Electronic ISBN: 978-3-030-77493-6

Copyright Year: 2021
DOI: https://doi.org/10.1007/978-3-030-77493-6_24

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