S-numbers of elementary operators on C*-algebras
M. Anoussis, V. Felouzis, I. G. Todorov

TL;DR
This paper investigates the behavior of s-numbers of elementary operators on C*-algebras, establishing conditions under which their approximation sequences belong to stable Calkin spaces, and providing a quantitative extension of Ylinen's result.
Contribution
It introduces new conditions linking s-numbers of elementary operators to stable Calkin spaces and extends Ylinen's results with quantitative bounds.
Findings
Sequences of s-numbers of tensor products belong to stable Calkin spaces under certain conditions.
The s-number sequences of sums of elementary operators are in a stable Calkin space if their components are.
A converse characterization is provided when the ideal of compact elements has finite spectrum.
Abstract
We study the s-numbers of elementary operators acting on C*-algebras. The main results are the following: If is any tensor norm and are such that the sequences of their singular numbers belong to a stable Calkin space then the sequence of approximation numbers of belongs to . If is a C*-algebra, is a stable Calkin space, is an s-number function, and are such that , for some faithful representation of then . The converse implication holds if and only if the ideal of compact elements of has finite spectrum. We also prove a quantitative version of a result of Ylinen.
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Taxonomy
TopicsAdvanced Operator Algebra Research · Advanced Topics in Algebra · Advanced Banach Space Theory
