On operators from separable reflexive spaces with asymptotic structure

• Autorzy: Bentuo Zheng
• Języki publikacji: EN

Abstrakty

EN

Let 1 < q < p < ∞ and q ≤ r ≤ p. Let X be a reflexive Banach space satisfying a lower-$ℓ_{q}$-tree estimate and let T be a bounded linear operator from X which satisfies an upper-$ℓ_{p}$-tree estimate. Then T factors through a subspace of $(∑ Fₙ)_{ℓ_{r}}$, where (Fₙ) is a sequence of finite-dimensional spaces. In particular, T factors through a subspace of a reflexive space with an $(ℓ_{p}, ℓ_{q})$ FDD. Similarly, let 1 < q < r < p < ∞ and let X be a separable reflexive Banach space satisfying an asymptotic lower-$ℓ_{q}$-tree estimate. Let T be a bounded linear operator from X which satisfies an asymptotic upper-$ℓ_{p}$-tree estimate. Then T factors through a subspace of $(∑ Gₙ)_{ℓ_{r}}$, where (Gₙ) is a sequence of finite-dimensional spaces. In particular, T factors through a subspace of a reflexive space with an asymptotic $(ℓ_{p},ℓ_{q})$ FDD.

Kategorie tematyczne

• 46B20: Geometry and structure of normed linear spaces
• 46B03: Isomorphic theory (including renorming) of Banach spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2008
• Tom: 185
• Numer: 1
• Strony: 87-98

Daty

wydano

2008

Twórcy

autor

Bentuo Zheng

• Department of Mathematics, The University of Texas at Austin, 1 University Station C1200, Austin, TX 78712-0257, U.S.A.

Identyfikatory

DOI

10.4064/sm185-1-6