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Weakly null sequences with upper estimates

100%

Freeman D.

Studia Mathematica

2008

tom 184

nr 1

79-102

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.

Upper and lower estimates for Schauder frames and atomic decompositions

51%

Beanland K., Freeman D., Liu R.

Fundamenta Mathematicae

2015

tom 231

nr 2

161-188

We prove that a Schauder frame for any separable Banach space is shrinking if and only if it has an associated space with a shrinking basis, and that a Schauder frame for any separable Banach space is shrinking and boundedly complete if and only if it has a reflexive associated space. To obtain these results, we prove that the upper and lower estimate theorems for finite-dimensional decompositions of Banach spaces can be extended and modified to Schauder frames. We show as well that if a separable infinite-dimensional Banach space has a Schauder frame, then it also has a Schauder frame which is not shrinking.

Ograniczanie wyników

1 Fundamenta Mathematicae

1 Studia Mathematica

2 Freeman D.

1 Beanland K.

1 Liu R.

1 2015

1 2008

Wyniki wyszukiwania

Weakly null sequences with upper estimates

Upper and lower estimates for Schauder frames and atomic decompositions