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arXiv · 1806.03595

Construction of k-g-fusion frames and their duals in Hilbert spaces

Vahid Sadri·Reza Ahmadi·Asghar Rahimi
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Abstract

Frames for operators or k-frames were recently considered by Gavruta (2012) in connection with atomic systems. Also generalized frames are important frames in the Hilbert space of bounded linear operators. Fusion frames, which are a special case of generalized frames have various applications. This paper introduces the concept of generalized fusion frames for operators aka k-g-fusion frames and we get some results for characterization of these frames. We further discuss on duals and Q-duals in connection with k-g-fusion frames. Also we obtain some useful identities for these frames. We also give several methods to construct k-g-fusion frames. The results of this paper can be used in sampling theory which are developed by g-frames and especially fusion frames. In the end, we discuss the stability of a more general perturbation for k-g-fusion frames.

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Vahid Sadri, Reza Ahmadi, Asghar Rahimi. 2018-06-10. Construction of k-g-fusion frames and their duals in Hilbert spaces. https://arxiv.org/abs/1806.03595

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