Derivations in algebras of operator-valued functions

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dc.creatorBer, A. F.
dc.creatorde Pagter, B.
dc.creatorSukochev, F. A.
dc.date2008-11-06
dc.date.accessioned2026-07-07T10:16:23Z
dc.date.available2026-07-07T10:16:23Z
dc.descriptionIn this paper we study derivations in subalgebras of $L_{0}^{wo}(ν;% \mathcal{L}(X)) $, the algebra of all weak operator measurable funtions $f:S\to \mathcal{L}(X) $, where $% \mathcal{L}(X) $ is the Banach algebra of all bounded linear operators on a Banach space $X$. It is shown, in particular, that all derivations on $L_{0}^{wo}(ν;\mathcal{L}(X)) $ are inner whenever $X$ is separable and infinite dimensional. This contrasts strongly with the fact that $L_{0}^{wo}(ν;\mathcal{L}(X)) $ admits non-trivial non-inner derivations whenever $X$ is finite dimensional and the measure $ν$ is non-atomic. As an application of our approach, we study derivations in various algebras of measurable operators affiliated with von Neumann algebras.
dc.description48 pages
dc.identifierhttps://arxiv.org/abs/0811.0902
dc.identifierhttp://arxiv.org/abs/0811.0902
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/173486
dc.subjectOperator Algebras
dc.subjectFunctional Analysis
dc.titleDerivations in algebras of operator-valued functions
dc.typetext

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