S-numbers of elementary operators on C*-algebras
| dc.creator | Anoussis, M. | |
| dc.creator | Felouzis, V. | |
| dc.creator | Todorov, I. G. | |
| dc.date | 2008-11-24 | |
| dc.date.accessioned | 2026-07-07T10:20:39Z | |
| dc.date.available | 2026-07-07T10:20:39Z | |
| dc.description | We study the s-numbers of elementary operators acting on C*-algebras. The main results are the following: If $τ$ is any tensor norm and $a,b\in B(H)$ are such that the sequences $s(a),s(b)$ of their singular numbers belong to a stable Calkin space $J$ then the sequence of approximation numbers of $a\otimes_τ b$ belongs to $J$. If $A$ is a C*-algebra, $J$ is a stable Calkin space, $s$ is an s-number function, and $a_i, b_i \in A,$ $i=1,...,m$ are such that $s(π(a_i)), s(π(b_i)) \in J$, $i=1,...,m$ for some faithful representation $π$ of $A$ then $s(\sum_{i=1}^{m} M_{a_i,b_i})\in J$. The converse implication holds if and only if the ideal of compact elements of $A$ has finite spectrum. We also prove a quantitative version of a result of Ylinen. | |
| dc.description | 25 pages | |
| dc.identifier | https://arxiv.org/abs/0811.3848 | |
| dc.identifier | http://arxiv.org/abs/0811.3848 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/174920 | |
| dc.subject | Operator Algebras | |
| dc.subject | 46L05; 47B47; 47L20 | |
| dc.title | S-numbers of elementary operators on C*-algebras | |
| dc.type | text |