University of MaraghehSahand Communications in Mathematical Analysis2322-580715120190701Some Properties of Continuous $K$-frames in Hilbert Spaces1691873596410.22130/scma.2018.85866.432ENGholamreza RahimlouDepartment of Mathematics, Shabestar Branch, Islamic Azad University, Shabestar, Iran.Reza AhmadiInstitute of Fundamental Sciences, University of Tabriz, Tabriz, Iran.Mohammad Ali JafarizadehFaculty of Physic, University of Tabriz,
Tabriz, Iran.Susan NamiFaculty of Physic, University of Tabriz,
Tabriz, Iran.Journal Article20180509The 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.http://scma.maragheh.ac.ir/article_35964_7a67421bd91eead5fc7d70935aa2f7cb.pdf