Groups of matrices with approximately submultiplicative spectra

TL;DR

This paper investigates an approximate version of the submultiplicative spectrum property in matrix semigroups, expanding understanding of spectral behavior under near-conditions.

Contribution

It introduces and analyzes an approximate form of the submultiplicative spectrum condition for matrix semigroups, extending classical spectral theory.

Findings

Characterization of approximate submultiplicative spectrum property

Conditions under which the property approximately holds

Implications for spectral analysis of matrix semigroups

Abstract

We say that a semigroup of matrices has a submultiplicative spectrum if the spectrum of the product of any two elements of the semigroup is contained in the product of the two spectra in question (as sets). In this note we explore an approximate version of this condition.