Currently displaying 1 – 8 of 8

Showing per page

Order by Relevance | Title | Year of publication

The dual form of the approximation property for a Banach space and a subspace

T. FigielW. B. Johnson — 2015

Studia Mathematica

Given a Banach space X and a subspace Y, the pair (X,Y) is said to have the approximation property (AP) provided there is a net of finite rank bounded linear operators on X all of which leave the subspace Y invariant such that the net converges uniformly on compact subsets of X to the identity operator. In particular, if the pair (X,Y) has the AP then X, Y, and the quotient space X/Y have the classical Grothendieck AP. The main result is an easy to apply dual formulation of this property. Applications...

Stochastic approximation properties in Banach spaces

V. P. FonfW. B. JohnsonG. PisierD. Preiss — 2003

Studia Mathematica

We show that a Banach space X has the stochastic approximation property iff it has the stochasic basis property, and these properties are equivalent to the approximation property if X has nontrivial type. If for every Radon probability on X, there is an operator from an L p space into X whose range has probability one, then X is a quotient of an L p space. This extends a theorem of Sato’s which dealt with the case p = 2. In any infinite-dimensional Banach space X there is a compact set K so that for...

Page 1

Download Results (CSV)