TY - JOUR ID - 35964 TI - Some Properties of Continuous $K$-frames in Hilbert Spaces JO - Sahand Communications in Mathematical Analysis JA - SCMA LA - en SN - 2322-5807 AU - Rahimlou, Gholamreza AU - Ahmadi, Reza AU - Jafarizadeh, Mohammad Ali AU - Nami, Susan AD - Department of Mathematics, Shabestar Branch, Islamic Azad University, Shabestar, Iran. AD - Institute of Fundamental Sciences, University of Tabriz, Tabriz, Iran. AD - Faculty of Physic, University of Tabriz, Tabriz, Iran. Y1 - 2019 PY - 2019 VL - 15 IS - 1 SP - 169 EP - 187 KW - k-frame KW - c-frame KW - ck-frame KW - Local cK-atoms DO - 10.22130/scma.2018.85866.432 N2 - 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. UR - https://scma.maragheh.ac.ir/article_35964.html L1 - https://scma.maragheh.ac.ir/article_35964_7a67421bd91eead5fc7d70935aa2f7cb.pdf ER -