Banach embedding properties of non-commutative L^p-spaces

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dc.creatorHaagerup, U.
dc.creatorRosenthal, H. P.
dc.creatorSukochev, F. A.
dc.date2000-05-15
dc.date.accessioned2026-07-07T04:35:17Z
dc.date.available2026-07-07T04:35:17Z
dc.descriptionLet N and M be von Neumann algebras. It is proved that L^p(N) does not Banach embed in L^p(M) for N infinite, M finite, 1 < or = p < 2. The following considerably stronger result is obtained (which implies this, since the Schatten p-class C_p embeds in L^p(N) for N infinite). Theorem: Let 1 < or = p < 2 and let X be a Banach space with a spanning set (x_{ij}) so that for some C < or = 1: (i) any row or column is C-equivalent to the usual ell^2-basis; (ii) (x_{i_k,j_k}) is C-equivalent to the usual ell^p-basis, for any i_1 < i_2 < ... and j_1 < j_2 < ... . Then X is not isomorphic to a subspace of L^p(M), for M finite. Complements on the Banach space structure of non-commutative L^p-spaces are obtained, such as the p-Banach-Saks property and characterizations of subspaces of L^p(M) containing ell^p isomorphically. The spaces L^p(N) are classified up to Banach isomorphism, for N infinite-dimensional, hyperfinite and semifinite, 1 < or = p< infty, p not= 2. It is proved that there are exactly thirteen isomorphism types; the corresponding embedding properties are determined for p < 2 via an eight level Hasse diagram. It is also proved for all 1 < or = p < infty that L^p(N) is completely isomorphic to L^p(M) if N and M are the algebras associated to free groups, or if N and M are injective factors of type III_lambda and III_{lambda'} for 0 < lambda, lambda' < or = 1.
dc.description54 pp., LaTeX
dc.identifierhttps://arxiv.org/abs/math/0005150
dc.identifierhttp://arxiv.org/abs/math/0005150
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/59200
dc.subjectFunctional Analysis
dc.subject46B20, 46L10, 46L52, 47L25 (Primary)
dc.titleBanach embedding properties of non-commutative L^p-spaces
dc.typetext

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