On operators which factor through $l_{p}$ or c₀

• Autorzy: Bentuo Zheng
• Języki publikacji: EN

Abstrakty

EN

Let 1 < p < ∞. Let X be a subspace of a space Z with a shrinking F.D.D. (Eₙ) which satisfies a block lower-p estimate. Then any bounded linear operator T from X which satisfies an upper-(C,p)-tree estimate factors through a subspace of $(∑Fₙ)_{l_{p}}$, where (Fₙ) is a blocking of (Eₙ). In particular, we prove that an operator from $L_{p}$ (2 < p < ∞) satisfies an upper-(C,p)-tree estimate if and only if it factors through $l_{p}$. This gives an answer to a question of W. B. Johnson. We also prove that if X is a Banach space with X* separable and T is an operator from X which satisfies an upper-(C,∞)-estimate, then T factors through a subspace of c₀.

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: 2006
• Tom: 176
• Numer: 2
• Strony: 177-190

Daty

wydano

2006

Twórcy

autor

Bentuo Zheng

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

Identyfikatory

DOI

10.4064/sm176-2-5