On Abstract Spectral Constants

TL;DR

This paper establishes bounds for unital homomorphisms related to spectral sets, unifying and refining key spectral constant results by notable mathematicians using extremal functions.

Contribution

It introduces a unified approach to spectral constants, recovering and refining several classical results through bounds involving extremal functions and vectors.

Findings

Unified proof of spectral constant results

Refinement of Crouzeix--Greenbaum's recent result

Bounds for unital homomorphisms in spectral set theory

Abstract

We prove bounds for a class of unital 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.