SMOOTHLY EMBEDDED SUBSPACES OF A BANACH SPACE

On separable Banach subspaces

We show that any infinite-dimensional Banach (or more generally, Fréchet) space contains linear subspaces of arbitrarily high Borel complexity which admit separable complete norms giving rise to the inherited Borel structure. © 2007 Elsevier Inc. All rights reserved.

On quasi-complemented subspaces of banach spaces.

. FA ] 2 9 M ar 1 99 3 TOPOLOGIES ON THE SET OF ALL SUBSPACES OF A BANACH SPACE AND RELATED QUESTIONS OF BANACH SPACE GEOMETRY

For a Banach space X we shall denote the set of all closed subspaces of X by G(X). In some kinds of problems it turned out to be useful to endow G(X) with a topology. The main purpose of the present paper is to survey results on two the most common topologies on G(X). The organization of this paper is as follows. In section 2 we introduce some definitions and notation. In sections 3 and 4 we in...

Strongly Proximinal Subspaces in Banach Spaces

We give descriptions of SSDand QP -points in C(K)-spaces and use this to characterize strongly proximinal subspaces of finite codimension in L1(μ). We provide some natural class of examples of strongly proximinal subspaces which are not necessarily finite codimensional. We also study transitivity of strong proximinal subspaces of finite codimension.

amenability of banach algebras

chapters 1 and 2 establish the basic theory of amenability of topological groups and amenability of banach algebras. also we prove that. if g is a topological group, then r (wluc (g)) (resp. r (luc (g))) if and only if there exists a mean m on wluc (g) (resp. luc (g)) such that for every wluc (g) (resp. every luc (g)) and every element d of a dense subset d od g, m (r)m (f) holds. chapter 3 inv...