Topological radicals, II. Applications to spectral theory of multiplication operators

TL;DR

This paper introduces new spectral radius techniques and tensor radical theory, applying them to analyze multiplication operators in Banach algebras and operator bimodules, leading to several new results.

Contribution

It develops the spectral radius and tensor radical theories and applies them to advance understanding of multiplication operators in Banach algebras.

Findings

New spectral radius techniques for multiplication operators

Development of tensor radical theory in this context

Numerous new results on multiplication operators in Banach algebras

Abstract

We develop the spectral radius technique and the theory of tensor radicals. As applications we obtain numerous results on mutiplication operators in Banach algebras and Operator bimodules.