Displaying similar documents to “A note on uniform or Banach density”

Weighted uniform densities

Rita Giuliano Antonini, Georges Grekos (2007)

Journal de Théorie des Nombres de Bordeaux

Similarity:

We introduce the concept of uniform weighted density (upper and lower) of a subset A of ℕ * , with respect to a given sequence of weights ( a n ) . This concept generalizes the classical notion of uniform density (for which the weights are all equal to 1). We also prove a theorem of comparison between two weighted densities (having different sequences of weights) and a theorem of comparison between a weighted uniform density and a weighted density in the classical sense. As a consequence, new...

A survey on the Szlenk index and some of its applications.

Gilles Lancien (2006)

RACSAM

Similarity:

We describe how the Szlenk index has been used in various areas of the geometry of Banach spaces. We cover the following domains of application of this notion: non existence of universal spaces, linear classification of C(K) spaces, descriptive set theory, renorming problems and non linear classification of Banach spaces.

Deformation of Banach spaces

Józef Banaś, Krzysztof Fraczek (1993)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

Using some moduli of convexity and smoothness we introduce a function which allows us to measure the deformation of Banach spaces. A few properties of this function are derived and its applicability in the geometric theory of Banach spaces is indicated.

A converse to Amir-Lindenstrauss theorem in complex Banach spaces.

Ondrej F. K. Kalenda (2006)

RACSAM

Similarity:

We show that a complex Banach space is weakly Lindelöf determined if and only if the dual unit ball of any equivalent norm is weak* Valdivia compactum. We deduce that a complex Banach space X is weakly Lindelöf determined if and only if any nonseparable Banach space isomorphic to a complemented subspace of X admits a projectional resolution of the identity. These results complete the previous ones on real spaces.