ar X iv : 0 70 5 . 43 04 v 1 [ m at h . FA ] 2 9 M ay 2 00 7 SLANTED MATRICES , BANACH FRAMES , AND SAMPLING
نویسنده
چکیده
In this paper we present a rare combination of abstract results on the spectral properties of slanted matrices and some of their very specific applications to frame theory and sampling problems. We show that for a large class of slanted matrices boundedness below of the corresponding operator in l for some p implies boundedness below in l for all p. We use the established result to enrich our understanding of Banach frames and obtain new results for irregular sampling problems. We also present a version of a non-commutative Wiener’s lemma for slanted matrices.
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