Descriptive properties of vector-valued affine functions
Let X be a compact convex set, extX stand for the set of extreme points of X, F be a Fréchet space and f : X → F be a strongly affine mapping. The aim of our paper is to investigate transfer of descriptive properties of f |extX to f , generalizing thus results from [3] and [2] to the vector-valued context. As a corollary of our results we obtain a vector-valued analogue of a result of J. Lindenstrauss and D.E. Wulbert on L1-preduals and answer positively Questions 10.6 and 10.7 from [1]. References [1] O. F. K. Kalenda and J. Spurný, Baire classes of affine vector-valued functions, Studia Math., 233 (2016), pp. 227–277. [2] P. Ludv́ık and J. Spurný, Descriptive properties of elements of biduals of Banach spaces, Studia Math., 209 (2012), pp. 71–99. [3] J. Saint-Raymond, Fonctions boréliennes sur un quotient, Bull. Sci. Math. (2), 100 (1976), pp. 141–147. Charles University, Faculty of Mathematics and Physics, Department of Mathematical Analysis, Sokolovská 83, 186 75, Praha 8, Czech Republic E-mail address: spurny@karlin.mff.cuni.cz