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arXiv · 1709.00585

Generalized frames and controlled operators in Hilbert space

Dongwei Li·Jinsong Leng
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Abstract

Controlled frames and g-frames were considered recently as generalizations of frames in Hilbert spaces. In this paper we generalize some of the known results in frame theory to controlled g-frames. We obtain some new properties of controlled g-frames and obtain new controlled g-frames by considering controlled g-frames for its components. And we obtain some new resolutions of the identity. Furthermore, we study the stabilities of controlled g-frames under small perturbations.

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Dongwei Li, Jinsong Leng. 2017-09-02. Generalized frames and controlled operators in Hilbert space. https://doi.org/10.1215/20088752-2019-0012

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