Weakly null sequences with upper estimates

• Autorzy: Daniel Freeman
• Języki publikacji: EN

Abstrakty

EN

We prove that if $(v_{i})$ is a seminormalized basic sequence and X is a Banach space such that every normalized weakly null sequence in X has a subsequence that is dominated by $(v_{i})$, then there exists a uniform constant C ≥ 1 such that every normalized weakly null sequence in X has a subsequence that is C-dominated by $(v_{i})$. This extends a result of Knaust and Odell, who proved this for the cases in which $(v_{i})$ is the standard basis for $ℓ_{p}$ or c₀.

Kategorie tematyczne

• 46B20: Geometry and structure of normed linear spaces
• 46B45: Banach sequence spaces
• 46B03: Isomorphic theory (including renorming) of Banach spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2008
• Tom: 184
• Numer: 1
• Strony: 79-102

Daty

wydano

2008

Twórcy

autor

Daniel Freeman

• Department of Mathematics, Texas A&M University, College Station, TX 77843-3368, U.S.A.

Identyfikatory

DOI

10.4064/sm184-1-4