$G$-Frames for operators in Hilbert spaces

Authors

  • Bahram Dastourian Department of Pure Mathematics, Ferdowsi University of Mashhad, Mashhad, P.O. Box 1159-91775, Iran.
  • Mohammad Janfada 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. Gu{a}vruc{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.

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Journal title

volume 08  issue 1

pages  1- 21

publication date 2017-10-01

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