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Descriptive properties of vector-valued affine functions

Volume 246 / 2019

Jiří Spurný Studia Mathematica 246 (2019), 233-256 MSC: 46A55, 46B25, 26A21, 54H05. DOI: 10.4064/sm170717-31-1 Published online: 8 October 2018

Abstract

Let $X$ be a compact convex set, $\operatorname {ext}X$ stand for the set of extreme points of $X$, $F$ be a Fréchet space and $f\colon X\to F$ be a strongly affine mapping. The aim of our paper is to investigate transfer of descriptive properties of $f|_{\operatorname {ext}X}$ to $f$, thus generalizing results of Saint-Raymond (1976) and Ludvik and Spurný (2012) to the vector-valued context. As a corollary, we obtain a vector-valued analogue of a result of J. Lindenstrauss and D. E. Wulbert (1969) on $L_1$-preduals and answer positively Questions 10.6 and 10.7 from Kalenda and Spurný (2016).

Authors

  • Jiří SpurnýCharles University
    Faculty of Mathematics and Physics
    Department of Mathematical Analysis
    Sokolovská 83
    186 75 Praha 8, Czech Republic
    e-mail

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