%0 Journal Article
%T Generalized Continuous Frames for Operators
%J Sahand Communications in Mathematical Analysis
%I University of Maragheh
%Z 2322-5807
%A .Shekhar, Chander
%A Bhati, Sunayana
%A Rathore, G.S.
%D 2020
%\ 06/01/2020
%V 17
%N 2
%P 185-201
%! Generalized Continuous Frames for Operators
%K Frames
%K $K$-frames
%K Continuous frames
%R 10.22130/scma.2018.97329.523
%X In this note, the notion of generalized continuous K- frame in a Hilbert space is defined. Examples have been given to exhibit the existence of generalized continuous $K$-frames. A necessary and sufficient condition for the existence of a generalized continuous $K$-frame in terms of its frame operator is obtained and a characterization of a generalized continuous $K$-frame for $ mathcal{H} $ with respect to $ mu $ is given. Also, a sufficient condition for a generalized continuous $K$-frame is given. Further, among other results, we prove that generalized continuous $K$-frames are invariant under a linear homeomorphism. Finally, keeping in mind the importance of perturbation theory in various branches of applied mathematics, we study perturbation of $K$-frames and obtain conditions for the stability of generalized continuous $K$-frames.
%U https://scma.maragheh.ac.ir/article_37409_6c5ddb5008c0e3934c7fff932837d13d.pdf