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Product integration in reflexive Banach spaces (1977)

Fitzgibbon, W. E.

Springer

Monatshefte für Mathematik 83 (1977), S. 113-119

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ISSN: 1436-5081

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics

Notes: 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.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF01534632

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