The algebraic numerical range as a spectral set in Banach algebras
Functional Analysis
2025-02-19 v2 Numerical Analysis
Numerical Analysis
Abstract
We investigate when the algebraic numerical range is a -spectral set in a Banach algebra. While providing several counterexamples based on classical ideas as well as combinatorial Banach spaces, we discuss positive results for matrix algebras and provide an absolute constant in the case of complex -matrices with the induced -norm. Furthermore, we discuss positive results for infinite-dimensional Banach algebras, including the Calkin algebra.
Keywords
Cite
@article{arxiv.2410.10678,
title = {The algebraic numerical range as a spectral set in Banach algebras},
author = {Hanna Blazhko and Daniil Homza and Felix L. Schwenninger and Jens de Vries and Michał Wojtylak},
journal= {arXiv preprint arXiv:2410.10678},
year = {2025}
}