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

Analysis Mathematica. 2024. Vol. 50. No. 3. P. 861–892.

Evseev N., Меновщиков А. В.

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 the sense that a binary relation replaces a mapping. The necessary and sufficient conditions for the boundedness of those operators are the main results of the paper.

Ключевые слова: direct integral, L^p-direct integral, Composition operator, Decomposable operator, Mixed-norm Lebesgue space