The composition of operatorvalued measurable functions is measurable
Authors:
A. Badrikian, G. W. Johnson and Il Yoo
Journal:
Proc. Amer. Math. Soc. 123 (1995), 18151820
MSC:
Primary 28B05; Secondary 46E40, 47A56, 47B99
DOI:
https://doi.org/10.1090/S00029939199512420729
MathSciNet review:
1242072
Fulltext PDF Free Access
Abstract  References  Similar Articles  Additional Information
Abstract: Given separable Frechet spaces, E, F, and G, let $\mathcal {L}(E,F),\mathcal {L}(F,G)$, and $\mathcal {L}(E,G)$ denote the space of continuous linear operators from E to F , F to G, and E to G, respectively. We topologize these spaces of operators by any one of a family of topologies including the topology of pointwise convergence and the topology of compact convergence. We will show that if $(X,\mathcal {F})$ is any measurable space and both $A:X \to \mathcal {L}(E,F)$ and $B:X \to \mathcal {L}(F,G)$ are Borelian, then the operator composition $BA:X \to \mathcal {L}(E,G)$ is also Borelian. Further, we will give several consequences of this result.

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Additional Information
Keywords:
Lusin space,
Souslin space,
operatorvalued measurable function,
measurability of operator composition,
strong operator measurability,
Frechet space,
Banach space,
topology of simple convergence,
topology of compact convergence
Article copyright:
© Copyright 1995
American Mathematical Society