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$G$-Frames for operators in Hilbert spaces

Journal: Sahand Communications in Mathematical Analysis (Vol.8, No. 1)

Publication Date:

Authors : ; ;

Page : 1-21

Keywords : $g$-atomic system; $g$-$K$-frame; $g$-$K$-dual; Perturbation;

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Abstract

$K$-frames as a generalization of frames were introduced by L. Gu{a}vruc{t}a to study atomic systems on Hilbert spaces which allows, in a stable way, to reconstruct elements from the range of the bounded linear operator $K$ in a Hilbert space. Recently some generalizations of this concept are introduced and some of its difference with ordinary frames are studied. In this paper, we give a new generalization of $K$-frames. After proving some characterizations of  generalized $K$-frames, new results are investigated  and some new perturbation results are established. Finally, we give several characterizations of $K$-duals.

Last modified: 2018-02-03 20:15:01