The Maurey extension property for Banach spaces with the Gordon-Lewis property and related structures

• Autorzy: P. G. Casazza , N. J. Nielsen
• Języki publikacji: EN

Abstrakty

EN

The main result of this paper states that if a Banach space X has the property that every bounded operator from an arbitrary subspace of X into an arbitrary Banach space of cotype 2 extends to a bounded operator on X, then every operator from X to an L₁-space factors through a Hilbert space, or equivalently $B(ℓ_{∞},X*) = Π₂(ℓ_{∞},X*)$. If in addition X has the Gaussian average property, then it is of type 2. This implies that the same conclusion holds if X has the Gordon-Lewis property (in particular X could be a Banach lattice) or if X is isomorphic to a subspace of a Banach lattice of finite cotype, thus solving the Maurey extension problem for these classes of spaces. The paper also contains a detailed study of the property of extending operators with values in $ℓ_{p}$-spaces, 1 ≤ p < ∞.

Kategorie tematyczne

• 46B03: Isomorphic theory (including renorming) of Banach spaces
• 46B07: Local theory of Banach spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2003
• Tom: 155
• Numer: 1
• Strony: 1-21

Daty

wydano

2003

Twórcy

autor

P. G. Casazza

• Department of Mathematics, University of Missouri, Columbia, MO 65211, U.S.A.

autor

N. J. Nielsen

• Department of Mathematics and Computer Science, University of Southern Denmark, Campusvej 55, DK-5230 Odense M, Denmark

Identyfikatory

DOI

10.4064/sm155-1-1