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Stochastic approximation properties in Banach spaces

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Fonf V., Johnson W., Pisier G., Preiss D.

Studia Mathematica

2003

tom 159

nr 1

103-119

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 any Radon probability on X there is an operator range of probability one that does not contain K.

Ograniczanie wyników

1 Studia Mathematica

1 Fonf V.

1 Johnson W.

1 Pisier G.

1 Preiss D.

1 2003

Wyniki wyszukiwania

Stochastic approximation properties in Banach spaces