Spectral Theory

Abstract

In this chapter we will study a pairA, Vof an order unit space and a base norm space in separating order and norm duality under the additional assumption that each exposed face of the distinguished baseKofVis projective. IfA,Vis such a pair, then we will say they satisfythe standing hypothesis.This hypothesis is satisfied when A is the self-adjoint part of a von Neumann algebra andVis the self -adjoint part of its predual, and also when A is a JBW-algebra and V is its predual. (In the former case, each norm closed face, and in particular each norm exposed face, is projective by virtue of (A 107). In the latter case, the same is true by Theorem 5.32.)