Dastourian, B., Janfada, M. (2017). $G$-Frames for operators in Hilbert spaces. Sahand Communications in Mathematical Analysis, 8(1), 1-21. doi: 10.22130/scma.2017.23646

Bahram Dastourian; Mohammad Janfada. "$G$-Frames for operators in Hilbert spaces". Sahand Communications in Mathematical Analysis, 8, 1, 2017, 1-21. doi: 10.22130/scma.2017.23646

Dastourian, B., Janfada, M. (2017). '$G$-Frames for operators in Hilbert spaces', Sahand Communications in Mathematical Analysis, 8(1), pp. 1-21. doi: 10.22130/scma.2017.23646

Dastourian, B., Janfada, M. $G$-Frames for operators in Hilbert spaces. Sahand Communications in Mathematical Analysis, 2017; 8(1): 1-21. doi: 10.22130/scma.2017.23646

^{}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.

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