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Upper and lower estimates for Schauder frames and atomic decompositions

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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 Beanland K.

1 Freeman D.

1 Liu R.

1 2015

Wyniki wyszukiwania

Upper and lower estimates for Schauder frames and atomic decompositions