%0 Journal Article
%T $G$-Frames for operators in Hilbert spaces
%J Sahand Communications in Mathematical Analysis
%I University of Maragheh
%Z 2322-5807
%A Dastourian, Bahram
%A Janfada, Mohammad
%D 2017
%\ 10/01/2017
%V 08
%N 1
%P 1-21
%! $G$-Frames for operators in Hilbert spaces
%K $g$-atomic system
%K $g$-$K$-frame
%K $g$-$K$-dual
%K Perturbation
%R 10.22130/scma.2017.23646
%X $K$-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 ofÂ generalized $K$-frames, new results are investigatedÂ and some new perturbation results are established. Finally, we give several characterizations of $K$-duals.
%U https://scma.maragheh.ac.ir/article_23646_5b6f187d7a7e622a7634cf56284bc2c6.pdf