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Article Dans Une Revue Transactions of the American Mathematical Society Année : 2009

Completely 1-complemented subspaces of Schatten spaces

Résumé

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.

Dates et versions

hal-00475222 , version 1 (21-04-2010)

Identifiants

Citer

Christian Le Merdy, Éric Ricard, Jean Roydor. Completely 1-complemented subspaces of Schatten spaces. Transactions of the American Mathematical Society, 2009, 361 (2), pp.849-887. ⟨10.1090/S0002-9947-08-04594-7⟩. ⟨hal-00475222⟩
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