Journal
RESULTS IN MATHEMATICS
Volume 77, Issue 3, Pages -Publisher
SPRINGER BASEL AG
DOI: 10.1007/s00025-022-01639-y
Keywords
Bessel sequence; frame; K-frame
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In this paper, we investigate finite extensions of Bessel sequences to K-frames in a separable Hilbert space H. We provide necessary and sufficient conditions for a Bessel sequence to be expanded to a K-frame and a Parseval K-frame by adding a finite number of elements in H. Additionally, we demonstrate that a frame can be extended to a Parseval K-frame under certain conditions.
In this paper, we study finite extensions of Bessel sequences to K-frames in a separable Hilbert space H. Precisely, we give some necessary and sufficient conditions for a Bessel sequence such that it can be expanded to a K-frame and a Parseval K-frame by adding finite number of elements in H. Also we show that under some conditions, a frame can be extended to a Parseval K-frame.
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