Published January 7, 2021 | Version v1
Publication

Banach function subspaces of L 1 of a vector measure and related Orlicz spaces

Description

Given a vector measure ν with values in a Banach space X, we consider the space L1(ν) of real functions which are integrable with respect to ν. We prove that every order continuous Banach function space Y continuously contained in L1(ν) is generated via a certain positive map ϱ related to ν and defined on X* x M, where X* is the dual space of X and M the space of measurable functions. This procedure provides a way of defining Orlicz spaces with respect to the vector measure ν.

Abstract

Ministerio de Ciencia y Tecnología BFM2003-06335-C03-01

Additional details

Created:
March 26, 2023
Modified:
November 29, 2023