## Illinois Journal of Mathematics

### Topological 0-1 laws for subspaces of a Banach space with a Schauder basis

Valentin Ferenczi

#### Abstract

For a Banach space $X$ with an (unconditional) basis, topological 0-1 law type dichotomies are stated for block-subspaces of $X$ as well as for subspaces of $X$ with a successive finite-dimensional decomposition on its basis. A uniformity principle for properties of block-sequences, results about block-homogeneity, and a possible method to construct a Banach space with an unconditional basis which has a complemented subspace without an unconditional basis, are deduced.

#### Article information

Source
Illinois J. Math., Volume 49, Number 3 (2005), 839-856.

Dates
First available in Project Euclid: 13 November 2009

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1258138222

Digital Object Identifier
doi:10.1215/ijm/1258138222

Mathematical Reviews number (MathSciNet)
MR2210262

Zentralblatt MATH identifier
1085.03036

#### Citation

Ferenczi, Valentin. Topological 0-1 laws for subspaces of a Banach space with a Schauder basis. Illinois J. Math. 49 (2005), no. 3, 839--856. doi:10.1215/ijm/1258138222. https://projecteuclid.org/euclid.ijm/1258138222