Stochastic approximation properties in Banach spaces

• Autorzy: V. P. Fonf , W. B. Johnson , G. Pisier , D. Preiss
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 46A35: Summability and bases
• 60B11: Probability theory on linear topological spaces
• 46E30: Spaces of measurable functions ( L p -spaces, Orlicz spaces, K\"othe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
• 46B25: Classical Banach spaces in the general theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2003
• Tom: 159
• Numer: 1
• Strony: 103-119

Daty

wydano

2003

Twórcy

autor

V. P. Fonf

• Ben-Gurion University of the Negev, P.O. Box 653, Beer-Sheva 84105, Israel

autor

W. B. Johnson

• Department of Mathematics, Texas A&M University, Department of Mathematics, College Station, TX 77843, U.S.A.

autor

G. Pisier

• Department of Mathematics, Texas A&M University, College Station, TX 77843, U.S.A.
• Equipe d'Analyse, Case 186, Université Paris VI, 75252 Paris, Cedex 05, France

autor

D. Preiss

• Department of Mathematics, University College London, London, Great Britain

Identyfikatory

DOI

10.4064/sm159-1-5