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Keywords
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Frame, K-frame, Hilbert–Schmidt frame, Hilbert–Schmidt
K-frame, Hilbert–Schmidt K-atomic system
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Abstract
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In this paper, we introduce Hilbert–Schmidt K-frames and Hilbert–Schmidt K-atomic systems, where K is a bounded operator on a Hilbert space, and we study the relationship between these two concepts. Also, Hilbert–Schmidt K-duals are defined and some of their properties are obtained, especially, we get the general form of the Hilbert–Schmidt K-duals for a given Hilbert–Schmidt K-frame. Moreover, some methods to construct Hilbert–Schmidt K-frames are presented and the stability of Hilbert Schmidt K-frames is considered.
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