On shrinking and boundedly complete Schauder frames of Banach spaces |
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Authors: | Rui Liu |
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Institution: | a Department of Mathematics and LPMC, Nankai University, Tianjin 300071, PR China b Department of Mathematics, Texas A&M University, College Station, TX 77843-3368, United States |
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Abstract: | This paper studies Schauder frames in Banach spaces, a concept which is a natural generalization of frames in Hilbert spaces and Schauder bases in Banach spaces. The associated minimal and maximal spaces are introduced, as are shrinking and boundedly complete Schauder frames. Our main results extend the classical duality theorems on bases to the situation of Schauder frames. In particular, we will generalize James' results on shrinking and boundedly complete bases to frames. Secondly we will extend his characterization of the reflexivity of spaces with unconditional bases to spaces with unconditional frames. |
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Keywords: | Associated space Duality theory Schauder frame |
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