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

Ferenczi, Valentin

Illinois J. Math., Tome 49 (2005) no. 2, p. 839-856 / Harvested from Project Euclid

Résumé

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.

Publié le : 2005-07-15
Classification: 46B15, 03E15, 46B03

@article{1258138222,
     author = {Ferenczi, Valentin},
     title = {Topological 0-1 laws for subspaces of a Banach space with a Schauder basis},
     journal = {Illinois J. Math.},
     volume = {49},
     number = {2},
     year = {2005},
     pages = { 839-856},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1258138222}
}

Ferenczi, Valentin. Topological 0-1 laws for subspaces of a Banach space with a Schauder basis. Illinois J. Math., Tome 49 (2005) no. 2, pp.  839-856. http://gdmltest.u-ga.fr/item/1258138222/