A Beurling theorem for noncommutative L^p

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dc.creatorBlecher, David P.
dc.creatorLabuschagne, Louis E.
dc.date2005-10-17
dc.date.accessioned2026-07-07T06:47:35Z
dc.date.available2026-07-07T06:47:35Z
dc.descriptionWe extend Beurling's invariant subspace theorem, by characterizing subspaces $K$ of the noncommutative $L^p$ spaces which are invariant with respect to Arveson's maximal subdiagonal algebras, sometimes known as noncommutative $H^\infty$. It is significant that a certain subspace, and a certain quotient, of $K$ are $L^p({\mathcal D})$-modules in the recent sense of Junge and Sherman, and therefore have a nice decomposition into cyclic submodules. We also give general inner-outer factorization formulae for elements in the noncommutative $L^p$. These facts generalize the classical ones, and should be useful in the future development of noncommutative $H^p$ theory. In addition, these results characterize maximal subdiagonal algebras.
dc.description16 pages
dc.identifierhttps://arxiv.org/abs/math/0510358
dc.identifierhttp://arxiv.org/abs/math/0510358
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/103698
dc.subjectOperator Algebras
dc.subjectFunctional Analysis
dc.titleA Beurling theorem for noncommutative L^p
dc.typetext

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