On a decomposition of Banach spaces

• Autorzy: Jakub Duda
• Języki publikacji: EN

Abstrakty

EN

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 This improves an earlier unpublished result of E. Matoušková.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.

Kategorie tematyczne

• 46B04: Isometric theory of Banach spaces
• 28A05: Classes of sets (Borel fields, σ -rings, etc.), measurable sets, Suslin sets, analytic sets

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2007
• Tom: 108
• Numer: 1
• Strony: 147-157

Daty

wydano

2007

Twórcy

autor

Jakub Duda

• Department of Mathematics, Weizmann Institute of Science, Rehovot 76100, Israel
• Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 186 75 Praha 8, Czech Republic

Identyfikatory

DOI

10.4064/cm108-1-13