Distances to spaces of affine Baire-one functions

Jiří Spurný¹

¹ Department of Mathematical Analysis Faculty of Mathematics and Physics Charles University Sokolovská 83 186 75 Praha 8, Czech Republic

Studia Mathematica, Tome 199 (2010) no. 1, pp. 23-41

Résumé

Let $E$ be a Banach space and let ${\cal B}_1(B_{E^*})$ and ${\mathfrak A}_1(B_{E^*})$ denote the space of all Baire-one and affine Baire-one functions on the dual unit ball $B_{E^*}$, respectively. We show that there exists a separable $L_1$-predual $E$ such that there is no quantitative relation between $\mathop{\rm dist}(f,{\cal B}_1(B_{E^*}))$ and $\mathop{\rm dist}(f,{\mathfrak A}_1(B_{E^*}))$, where $f$ is an affine function on $B_{E^*}$. If the Banach space $E$ satisfies some additional assumption, we prove the existence of some such dependence.

Détail

DOI : 10.4064/sm199-1-3

Keywords: banach space cal * mathfrak * denote space baire one affine baire one functions dual unit ball * respectively there exists separable predual there quantitative relation between mathop dist cal * mathop dist mathfrak * where affine function * banach space satisfies additional assumption prove existence dependence