Baire classes of complex L-1-preduals

Abstract

Let X be a complex L 1-predual, non-separable in general. We investigate extendability of complex-valued bounded homogeneous Baire-α functions on the set ext B X* of the extreme points of the dual unit ball B X* to the whole unit ball B X*. As a corollary we show that, given α ∈ [1, ω 1), the intrinsic α-th Baire class of X can be identified with the space of bounded homogeneous Baire-α functions on the set ext B X* when ext B X* satisfies certain topological assumptions. The paper is intended to be a complex counterpart to the same authors’ paper: Baire classes of non-separable L 1-preduals (2015). As such it generalizes former work of Lindenstrauss and Wulbert (1969), Jellett (1985), and ourselves (2014), (2015).