Topological radicals, I. Basic properties, tensor products and joint quasinilpotence

TL;DR

This paper introduces the foundational properties of topological radicals, explores their relation to tensor products, and develops a theory connecting radicals to joint tensor radius, advancing the mathematical understanding of operator theory.

Contribution

It presents the first comprehensive study of topological radicals, focusing on their basic properties, tensor product interactions, and the novel concept of joint tensor radius.

Findings

Established fundamental properties of topological radicals.

Developed a theory linking radicals to joint tensor radius.

Laid groundwork for future research in operator theory and radicals.

Abstract

The work starts a series of papers on topological radicals and their applications. Among other results we present a theory of radicals related to the joint tensor radius.