Distances to spaces of affine Baire-one functions

• Autorzy: Jiří Spurný
• Języki publikacji: EN

Abstrakty

EN

Let E be a Banach space and let $ℬ₁(B_{E*})$ and $𝔄₁(B_{E*})$ 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 L₁-predual E such that there is no quantitative relation between $dist(f,ℬ₁(B_{E*}))$ and $dist(f,𝔄₁(B_{E*}))$, 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.

Kategorie tematyczne

• 46B99: None of the above, but in this section
• 52A07: Convex sets in topological vector spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2010
• Tom: 199
• Numer: 1
• Strony: 23-41

Daty

wydano

2010

Twórcy

autor

Jiří Spurný

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

Identyfikatory

DOI

10.4064/sm199-1-3