Document Type : Research Paper

Authors

1 Department of Mathematics, Shabestar Branch, Islamic Azad University, Shabestar, Iran.

2 Institute of Fundamental Sciences, University of Tabriz, Tabriz, Iran.

3 Faculty of Physic, University of Tabriz, Tabriz, Iran.

Abstract

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.

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