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Extension of smooth subspaces in Lindenstrauss spaces

100%

Fonf V., Wojtaszczyk P.

Studia Mathematica

2014

tom 222

nr 2

157-163

It follows from our earlier results [Israel J. Math., to appear] that in the Gurariy space G every finite-dimensional smooth subspace is contained in a bigger smooth subspace. We show that this property does not characterise the Gurariy space among Lindenstrauss spaces and we provide various examples to show that C(K) spaces do not have this property.

Stochastic approximation properties in Banach spaces

81%

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

2 Studia Mathematica

2 Fonf V.

1 Johnson W.

1 Pisier G.

1 Preiss D.

1 Wojtaszczyk P.

1 2014

1 2003

Wyniki wyszukiwania

Extension of smooth subspaces in Lindenstrauss spaces

Stochastic approximation properties in Banach spaces