Document Type: Research Paper

**Authors**

Department of Pure Mathematics, Ferdowsi University of Mashhad, Mashhad, P.O. Box 1159-91775, Iran.

**Abstract**

$K$-frames as a generalization of frames were introduced by L. G\u{a}vru\c{t}a to study atomic systems on Hilbert spaces which allows, in a stable way, to reconstruct elements from the range of the bounded linear operator $K$ in a Hilbert space. Recently some generalizations of this concept are introduced and some of its difference with ordinary frames are studied. In this paper, we give a new generalization of $K$-frames. After proving some characterizations of generalized $K$-frames, new results are investigated and some new perturbation results are established. Finally, we give several characterizations of $K$-duals.

**Keywords**

**Main Subjects**

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