Pointwise convergence for semigroups in vector-valued $L^p$ spaces

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dc.creatorTaggart, Robert J.
dc.date2007-05-31
dc.date2008-02-28
dc.date.accessioned2026-07-07T09:23:26Z
dc.date.available2026-07-07T09:23:26Z
dc.descriptionSuppose that T_t is a symmetric diffusion semigroup on L^2(X) and consider its tensor product extension to the Bochner space L^p(X,B), where B belongs to a certain broad class of UMD spaces. We prove a vector-valued version of the Hopf--Dunford--Schwartz ergodic theorem and show that this extends to a maximal theorem for analytic continuations of the semigroup's extension to L^p(X,B). As an application, we show that such continuations exhibit pointwise convergence.
dc.descriptionIn version2 we correct the error present in version 1 as well as removing one of the hypotheses of the main theorem. Section 2 is also rewritten
dc.identifierhttps://arxiv.org/abs/0705.4510
dc.identifierhttp://arxiv.org/abs/0705.4510
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/155733
dc.subjectFunctional Analysis
dc.subjectSpectral Theory
dc.subject47D03
dc.titlePointwise convergence for semigroups in vector-valued $L^p$ spaces
dc.typetext

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