Geodesic
Upper and lower estimates for Schauder frames and atomic decompositions
Kevin Beanland 1   ; Daniel Freeman 2   ; Rui Liu 3
1 Washington and Lee University 204 W. Washington St. Lexington, VA 24450, U.S.A.
2 Department of Mathematics and Computer Science Saint Louis University St. Louis, MO 63103, U.S.A.
3 Department of Mathematics and LPMC Nankai University Tianjin 300071, P.R. China and Department of Mathematics Texas A&M University College Station, TX 77843, U.S.A.
Fundamenta Mathematicae, Tome 231 (2015) no. 2, pp. 161-188 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/fm231-2-4
Keywords: prove schauder frame separable banach space shrinking only has associated space shrinking basis schauder frame separable banach space shrinking boundedly complete only has reflexive associated space obtain these results prove upper lower estimate theorems finite dimensional decompositions banach spaces extended modified schauder frames separable infinite dimensional banach space has schauder frame has schauder frame which shrinking

Kevin Beanland  1   ; Daniel Freeman  2   ; Rui Liu  3

1 Washington and Lee University 204 W. Washington St. Lexington, VA 24450, U.S.A.
2 Department of Mathematics and Computer Science Saint Louis University St. Louis, MO 63103, U.S.A.
3 Department of Mathematics and LPMC Nankai University Tianjin 300071, P.R. China and Department of Mathematics Texas A&M University College Station, TX 77843, U.S.A. 
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 and atomic decompositions
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Kevin Beanland; Daniel Freeman; Rui Liu. Upper and lower estimates for Schauder frames
 and atomic decompositions. Fundamenta Mathematicae, Tome 231 (2015) no. 2, pp. 161-188. doi: 10.4064/fm231-2-4

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