Yet another generalization of frames and Riesz bases
نویسندگان
چکیده
منابع مشابه
G-Frames, g-orthonormal bases and g-Riesz bases
G-Frames in Hilbert spaces are a redundant set of operators which yield a representation for each vector in the space. In this paper we investigate the connection between g-frames, g-orthonormal bases and g-Riesz bases. We show that a family of bounded operators is a g-Bessel sequences if and only if the Gram matrix associated to its denes a bounded operator.
متن کاملFrames, Riesz Bases and Double Infinite Matrices
In this paper we have used double infinite matrix A = (ailjk) of real numbers to define the A-frame. Some results on Riesz basis and A-frame also have been studied. This Work is motivated from the work of Moricz and Rhoades [7]. 2001 AMS Classification. Primary 41A17, Secondary 42C15.
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Abstract G-frames are generalized frames which include ordinary frames, bounded invertible linear operators, as well as many recent generalizations of frames, e.g., bounded quasi-projectors and frames of subspaces. G-frames are natural generalizations of frames and provide more choices on analyzing functions from frame expansion coefficients. We give characterizations of g-frames and prove that...
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We provide a unifying axiomatics for Rényi’s entropy and non–extensive entropy of Tsallis. It is shown that the resulting entropy coincides with Csiszár’s measure of directed divergence known from communication theory.
متن کاملg-frames, g-orthonormal bases and g-riesz bases
g-frames in hilbert spaces are a redundant set of operators which yield a repre-sentation for each vector in the space. in this paper we investigate the connection betweeng-frames, g-orthonormal bases and g-riesz bases. we show that a family of bounded opera-tors is a g-bessel sequences if and only if the gram matrix associated to its de nes a boundedoperator.
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ژورنال
عنوان ژورنال: Involve, a Journal of Mathematics
سال: 2009
ISSN: 1944-4176
DOI: 10.2140/involve.2009.2.397