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Języki publikacji
Abstrakty
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.
Słowa kluczowe
Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
161-188
Opis fizyczny
Daty
wydano
2015
Twórcy
autor
- Washington and Lee University, 204 W. Washington St., Lexington, VA 24450, U.S.A.
autor
- Department of Mathematics, and Computer Science, Saint Louis University, St. Louis, MO 63103, U.S.A.
autor
- Department of Mathematics and LPMC, Nankai University, Tianjin 300071, P.R. China
- Department of Mathematics, Texas A&M University, College Station, TX 77843, U.S.A.
Bibliografia
Typ dokumentu
Bibliografia
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Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_4064-fm231-2-4