The $H^{\infty}-$calculus and sums of closed operators

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dc.creatorKalton, N. J.
dc.creatorWeis, L.
dc.date2000-10-15
dc.date.accessioned2026-07-07T04:38:03Z
dc.date.available2026-07-07T04:38:03Z
dc.descriptionWe develop a very general operator-valued functional calculus for operators with an $H^{\infty}-$calculus. We then apply this to the joint functional calculus of two commuting sectorial operators when one has an $H^{\infty}$calculus. Using this we prove theorem of Dore-Venni type on sums of commuting sectorial operators and apply our results to the problem of $L_p-$maximal regularity. Our main assumption is the R-boundedness of certain sets of operators, and therefore methods from the geometry of Banach spaces are essential here. In the final section we exploit the special Banach space structure of $L_1-$spaces and $C(K)-$spaces, to obtain some more detailed results in this setting.
dc.description26 pages
dc.identifierhttps://arxiv.org/abs/math/0010155
dc.identifierhttp://arxiv.org/abs/math/0010155
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/60137
dc.subjectFunctional Analysis
dc.subject47A60; 47D06
dc.titleThe $H^{\infty}-$calculus and sums of closed operators
dc.typetext

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