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Product integration in reflexive Banach spaces

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Abstract

LetX denote a reflexive Banach space and {A(t)|t∈[0,T]} a time dependent family of accretive operators defined onX. Conditions are placed on {A(t)|t∈[0,T]} which are sufficient to guarantee the existence of solutions to the Cauchy initial value problem:u′(t,x)+A(t)u(t,x)=0; u(0,x)=x. These solutions are obtained via the method of product integration; however limits for the infinite product are taken with respect to the weak topology.

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  1. Department of Mathematics, University of Houston, Cullen Boulevard, 77004, Houston, TX, U.S.A.

    W. E. Fitzgibbon

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  1. W. E. Fitzgibbon
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Fitzgibbon, W.E. Product integration in reflexive Banach spaces. Monatshefte für Mathematik 83, 113–119 (1977). https://doi.org/10.1007/BF01534632

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  • DOI: https://doi.org/10.1007/BF01534632

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