Completely 1-complemented subspaces of Schatten spaces

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dc.creatorMerdy, Christian Le
dc.creatorRicard, Eric
dc.creatorRoydor, Jean
dc.date2008-03-31
dc.date2009-01-08
dc.date.accessioned2026-07-07T12:26:54Z
dc.date.available2026-07-07T12:26:54Z
dc.descriptionWe 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.
dc.descriptionTo 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
dc.identifierhttps://arxiv.org/abs/0803.4408
dc.identifierhttp://arxiv.org/abs/0803.4408
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/215029
dc.subjectOperator Algebras
dc.subjectFunctional Analysis
dc.subject46L07; 46L89; 17C65
dc.titleCompletely 1-complemented subspaces of Schatten spaces
dc.typetext

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