%0 Journal Article
%T Some Properties of Continuous $K$-frames in Hilbert Spaces
%J Sahand Communications in Mathematical Analysis
%I University of Maragheh
%Z 2322-5807
%A Rahimlou, Gholamreza
%A Ahmadi, Reza
%A Jafarizadeh, Mohammad Ali
%A Nami, Susan
%D 2019
%\ 07/01/2019
%V 15
%N 1
%P 169-187
%! Some Properties of Continuous $K$-frames in Hilbert Spaces
%K $K$-frame
%K c-frame
%K c$K$-frame
%K Local c$K$-atoms
%R 10.22130/scma.2018.85866.432
%X The theory of continuous frames in Hilbert spaces is extended, by using the concepts of measure spaces, in order to get the results of a new application of operator theory. The $K$-frames were introduced by G$breve{mbox{a}}$vruta (2012) for Hilbert spaces to study atomic systems with respect to a bounded linear operator. Due to the structure of $K$-frames, there are many differences between $K$-frames and standard frames. $K$-frames, which are a generalization of frames, allow us in a stable way, to reconstruct elements from the range of a bounded linear operator in a Hilbert space. In this paper, we get some new results on the continuous $K$-frames or briefly c$K$-frames, namely some operators preserving and some identities for c$K$-frames. Also, the stability of these frames are discussed.
%U http://scma.maragheh.ac.ir/article_35964_7a67421bd91eead5fc7d70935aa2f7cb.pdf