Factorization of operators on $C^*$-algebras

Details Factorization of operators on $C^*$-algebras Factorization of operators on $C^*$-algebras

1997-02-25

arxiv.org/abs/math/9702217v1

Mathematics

Functional Analysis

Scientific paper

Let $A$ be a $C^*$-algebra. It is shown that every absolutely summing operator from $A$ into $\ell_2$ factors through a Hilbert space operator that belongs to the 4-Schatten- von Neumann class. We also provide finite dimensinal examples that show that one can not improve the 4-Schatten-von Neumann class to $p$-Schatten von Neumann class for any $p<4$. As application, we prove that there exists a modulus of capacity $\epsilon \to N(\epsilon)$ so that if $A$ is a $C^*$-algebra and $T \in \Pi_1(A,\ell_2)$ with $\pi_1(T)\leq 1$, then for every $\epsilon >0$, the $\epsilon$-capacity of the image of the unit ball of $A$ under $T$ does not exceed $N(\epsilon)$. This aswers positively a question raised by Pe\l czynski.

Affiliated with

Also associated with

No associations

Rating

Factorization of 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 Factorization of operators on $C^*$-algebras, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Factorization of operators on $C^*$-algebras will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-75350