arXiv 0803.44082008-03math.OAmath.FA

Completely 1-complemented subspaces of Schatten spaces

Christian Le Merdy, Eric Ricard, Jean Roydor

备注：: To be pubished in the Transactions of the American Mathematical Society. This revised version contains minor corrections. More specifically, Remark 5.5, Proposition 7.3 and its proof, as well as Remark 7.4 have been modified

英文摘要：

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.

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