On a decomposition of Banach spaces

Jakub Duda. "On a decomposition of Banach spaces." Colloquium Mathematicae 108.1 (2007): 147-157. <http://eudml.org/doc/286064>.

@article{JakubDuda2007,
abstract = {By using D. Preiss' approach to a construction from a paper by J. Matoušek and E. Matoušková, and some results of E. Matoušková, we prove that we can decompose a separable Banach space with modulus of convexity of power type p as a union of a ball small set (in a rather strong symmetric sense) and a set which is Aronszajn null. This improves an earlier unpublished result of E. Matoušková. As a corollary, in each separable Banach space with modulus of convexity of power type p, there exists a closed nonempty set A and a Borel non-Haar null set Q such that no point from Q has a nearest point in A. Another corollary is that ℓ₁ and L₁ can be decomposed as unions of a ball small set and an Aronszajn null set.},
author = {Jakub Duda},
journal = {Colloquium Mathematicae},
keywords = {ball small sets; Aronszajn null sets; superreflexive spaces},
language = {eng},
number = {1},
pages = {147-157},
title = {On a decomposition of Banach spaces},
url = {http://eudml.org/doc/286064},
volume = {108},
year = {2007},
}

TY - JOUR
AU - Jakub Duda
TI - On a decomposition of Banach spaces
JO - Colloquium Mathematicae
PY - 2007
VL - 108
IS - 1
SP - 147
EP - 157
AB - By using D. Preiss' approach to a construction from a paper by J. Matoušek and E. Matoušková, and some results of E. Matoušková, we prove that we can decompose a separable Banach space with modulus of convexity of power type p as a union of a ball small set (in a rather strong symmetric sense) and a set which is Aronszajn null. This improves an earlier unpublished result of E. Matoušková. As a corollary, in each separable Banach space with modulus of convexity of power type p, there exists a closed nonempty set A and a Borel non-Haar null set Q such that no point from Q has a nearest point in A. Another corollary is that ℓ₁ and L₁ can be decomposed as unions of a ball small set and an Aronszajn null set.
LA - eng
KW - ball small sets; Aronszajn null sets; superreflexive spaces
UR - http://eudml.org/doc/286064
ER -