J. M. Almira; U. Luther : Compactness and Generalized Approximation Spaces

Author(s) :

J. M. Almira; U. Luther

Title :

Compactness and Generalized Approximation Spaces

Electronic source :

[gzipped ps-file] 178 kB

Preprint series

Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 2000-18, 2000

Mathematics Subject Classification :

41A65 [ Abstract approximation theory ]

46B99 [ Normed linear spaces and Banach spaces ]

Abstract :

We show that generalized approximation spaces can be used to desbribe the relative compact sets of Banach spaces. This leads to compactness and convergence criteria in the approximation spaces themselves. If these spaces can be described with the help of moduli of smoothness, then the criteria can be formulated in terms of the moduli. As applications we give an easy proof of a Bernstein theorem, a criterion for compactness in Sobolev type spaces, and a generalization of Simon's compactness criterion for subsets of L^p-spaces of Banach-space-valued functions.

Keywords :

Approximation spaces, Besov spaces, Compactness, Moduli of smoothness

Language :

english

Publication time :

12/2000