Decomposable operators acting between distinct $L^p$-direct integrals of Banach spaces (1902.02983v3)

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.