A non-commutative Yosida-Hewitt theorem and convex sets of measurable operators closed locally in measure

Abstract

We present a non-commutative extension of the classical Yosida-Hewitt decomposition of a finitely additive measure into its σ-additive and singular parts. Several applications are given to the characterisation of bounded convex sets in Banach spaces of measurable operators which are closed locally in measure. © Springer 2005.