Completely 1-complemented subspaces of Schatten spaces

Details Completely 1-complemented subspaces of Schatten spaces Completely 1-complemented subspaces of Schatten spaces

2008-03-31

arxiv.org/abs/0803.4408v2

Mathematics

Operator Algebras

To be pubished in the Transactions of the American Mathematical Society. This revised version contains minor corrections. More

Scientific paper

We consider the Schatten spaces S^p in the framework of operator space theory and for any $1\leq p\not=2<\infty$, we characterize the completely 1-complemented subspaces of S^p. They turn out to be the direct sums of spaces of the form S^p(H,K), where H,K are Hilbert spaces. This result is related to some previous work of Arazy-Friedman giving a description of all 1-complemented subspaces of S^p in terms of the Cartan factors of types 1-4. We use operator space structures on these Cartan factors regarded as subspaces of appropriate noncommutative L^p-spaces. Also we show that for any $n\geq 2$, there is a triple isomorphism on some Cartan factor of type 4 and of dimension 2n which is not completely isometric, and we investigate L^p-versions of such isomorphisms.

Affiliated with

Also associated with

No associations

Rating

Completely 1-complemented subspaces of Schatten spaces 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 Completely 1-complemented subspaces of Schatten spaces, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Completely 1-complemented subspaces of Schatten spaces will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-197214