Measurable bundles of compact operators (Q2784960)

The authors consider operators on Banach-Kantorovich spaces. The latter are defined as real vector spaces which are in a certain sense complete with respect to a norm with values in the space \(L_0\) of measurable real functions on a measurable space \(\Omega\). It is known that every Banach-Kantorovich space is isomorphic to the space of measurable sections of some measurable Banach bundle, that is, roughly speaking, to a space of vector-functions on \(\Omega\) with values in a Banach space \(X\). Correspondingly, each \(L_0\)-linear operator can be decomposed into a family of operators on \(X\). The authors describe a class of compact operators on a Banach-Kantorovich space for which operators appearing in the above decomposition are compact.