A characterization of the local Radon-Nikodým property by tensor products

Donald P. Story

Vol. 91 (1980), No. 1, 219–222

DOI: 10.2140/pjm.1980.91.219

Abstract

In this paper, results are presented that characterize the collection of all vector valued measures expressible as an indefinite Bochner integral. More precisely, if X is a Banach space, an X-valued vector measure, τ, defined on a measurable space (S,Ω) is expressible as a Bochner integral if and only if τ belongs to ca(S,Ω)⊗ _πX, where ⊗ _π denotes the strong (or projective) tensor product of two Banach spaces. Other related results are given.

Mathematical Subject Classification 2000

Primary: 46G10

Secondary: 28B05

Milestones

Received: 8 May 1979

Published: 1 November 1980