S-numbers of elementary operators on C*-algebras

Details S-numbers of elementary operators on C*-algebras S-numbers of elementary operators on C*-algebras

2008-11-24

arxiv.org/abs/0811.3848v1

Mathematics

Operator Algebras

25 pages

Scientific paper

We study the s-numbers of elementary operators acting on C*-algebras. The main results are the following: If $\tau$ 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 $a\otimes_{\tau} b$ 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 $s(\pi(a_i)), s(\pi(b_i)) \in J$, $i=1,...,m$ for some faithful representation $\pi$ 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.

Affiliated with

Also associated with

No associations

Rating

S-numbers of elementary operators on C*-algebras does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with S-numbers of elementary operators on C*-algebras, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and S-numbers of elementary operators on C*-algebras will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-645053