BAIRE CLASSES OF NON-SEPARABLE L-1-PREDUALS

作者：Ludvik Pavel; Spurny Jiri^*

来源：The Quarterly Journal of Mathematics, 2015, 66(1): 251-263.

DOI：10.1093/qmath/hau007

Let X be an L-1-predual, non-separable in general. We show that the intrinsic Baire classes of X can be identified with the spaces of odd Baire functions on the set ext B-X* of the extreme points of the dual unit ball B-X* in the case when ext BX* satisfies some topological assumptions. This generalizes results of Lindenstrauss and Wulbert from [On the classification of the Banach spaces whose duals are L-1 spaces, J. Funct. Anal. 4 (1969), 332-349], Jellett in [On affine extensions of continuous functions defined on the extreme boundary of a Choquet simplex, Quart. J. Math. Oxford Ser. (1) 36 (1985), 71-73] and of ours in [Baire Classes of L-1-preduals and C*-algebras, 2013. http://www.karlin.mff.cuni.cz/spurny/articles.php].

• 出版日期2015-3