Decomposable operators acting between distinct $L^p$-direct integrals of Banach spaces

Abstract

The notion of decomposable operators acting between distinct $L^p$-direct integrals of Banach spaces is introduced. We show that these operators generalize the composition operator, in sense that a mapping is replaced by a binary relation. The necessary and sufficient conditions for the boundedness of those operators are the main results of the paper.

26 pages, 7 figures

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