This is an announcement for the paper "Completely 1-complemented subspaces of Schatten spaces" by Christian Le Merdy, Eric Ricard, and Jean Roydor.

Abstract: 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.

Archive classification: math.FA math.OA

Mathematics Subject Classification: 46L07; 46L89; 17C65

Remarks: To be pubished in the Transactions of the American Mathematical

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http://front.math.ucdavis.edu/0803.4408

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http://arXiv.org/abs/0803.4408

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