The algebraic numerical range as a spectral set in Banach algebras

Hanna Blazhko, Daniil Homza, Felix L. Schwenninger, Jens de Vries, Michał Wojtylak

Research output: Working paperPreprintAcademic

36 Downloads (Pure)

Abstract

We investigate when the algebraic numerical range is a C-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 2×2-matrices with the induced 1-norm. Furthermore, we discuss positive results for infinite-dimensional Banach algebras, including the Calkin algebra.
Original languageEnglish
PublisherArXiv.org
Number of pages22
DOIs
Publication statusPublished - 14 Oct 2024

Keywords

  • math.FA
  • cs.NA
  • math.NA
  • 47A25, 47A12, 47B48, 15A60

Fingerprint

Dive into the research topics of 'The algebraic numerical range as a spectral set in Banach algebras'. Together they form a unique fingerprint.

Cite this