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Weighted Hardy Spaces Over the Unit Ball: The Freely Noncommutative and Commutative Settings Read chapter Read first chapter

2024 | OriginalPaper | Chapter

On Abstract Spectral Constants

Authors : Felix L. Schwenninger, Jens de Vries

Published in: Operator and Matrix Theory, Function Spaces, and Applications

Publisher: Springer Nature Switzerland

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Abstract

We prove bounds for a class of homomorphisms arising in the study of spectral sets, by involving extremal functions and vectors. These are used to recover three celebrated results on spectral constants by Crouzeix–Palencia, Okubo–Ando and von Neumann in a unified way and to refine a recent result by Crouzeix–Greenbaum.

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Footnotes
1
In the literature a \(\kappa \)-spectral set is typically instead defined by requiring that (1) holds for all rational functions p with poles off \(W^{-}\) and such that the spectrum of M is contained in \(W^{-}\). For the applications we have in mind, considering polynomials is however sufficient.
 
2
This mapping, however, fails to be multiplicative in general.
 
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Metadata
Title
On Abstract Spectral Constants
Authors
Felix L. Schwenninger
Jens de Vries
Copyright Year
2024
Book
Operator and Matrix Theory, Function Spaces, and Applications

Print ISBN: 978-3-031-50612-3

Electronic ISBN: 978-3-031-50613-0

Copyright Year: 2024

DOI
https://doi.org/10.1007/978-3-031-50613-0_15

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