The Radon-Nikodym theorem for vector measures and integral representation of operators on Banach function spaces

摘要

A well known vector measure version of the Radon-Nikodym theorem --comparing two vector measures-- can also be interpreted in terms of factorization of an operator --the one associated to the first measure-- through the one associated to the second one. Using several results published in recent years, we show the factorization version of this Radon-Nikodym theorem and its applications in the setting of the Operator Theory and the Harmonic Analysis.