Title: Decomposable operators on Lp-direct integrals
Abstract: If in space Lp(Ω, X) of vector-valued functions we replace a Banach space X by a family of Banach spaces Xω then we arrive at the concept of Lp-direct integral. In the course of the talk, we introduce and study decomposable operator M:Lp(T, Wt) -> Lq(S, Vs) i.e. which induced by operators P(t,s):Wt->Vs. The necessary and sufficient conditions for boundedness of operator M are provided.
