Distances to spaces of affine Baire-one functions

Jiří Spurný. "Distances to spaces of affine Baire-one functions." Studia Mathematica 199.1 (2010): 23-41. <http://eudml.org/doc/285666>.

@article{JiříSpurný2010,
abstract = {Let E be a Banach space and let $ℬ₁(B_\{E*\})$ and $₁(B_\{E*\})$ 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 L₁-predual E such that there is no quantitative relation between $dist(f,ℬ₁(B_\{E*\}))$ and $dist(f,₁(B_\{E*\}))$, 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.},
author = {Jiří Spurný},
journal = {Studia Mathematica},
keywords = {affine function; Baire measurable function; Baire-one function; extreme points; fragmented function; -predual; simplex; strongly affine function},
language = {eng},
number = {1},
pages = {23-41},
title = {Distances to spaces of affine Baire-one functions},
url = {http://eudml.org/doc/285666},
volume = {199},
year = {2010},
}

TY - JOUR
AU - Jiří Spurný
TI - Distances to spaces of affine Baire-one functions
JO - Studia Mathematica
PY - 2010
VL - 199
IS - 1
SP - 23
EP - 41
AB - Let E be a Banach space and let $ℬ₁(B_{E*})$ and $₁(B_{E*})$ 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 L₁-predual E such that there is no quantitative relation between $dist(f,ℬ₁(B_{E*}))$ and $dist(f,₁(B_{E*}))$, 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.
LA - eng
KW - affine function; Baire measurable function; Baire-one function; extreme points; fragmented function; -predual; simplex; strongly affine function
UR - http://eudml.org/doc/285666
ER -