Generalized Continuous Frames for Operators

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Shekhar Chander; Bhati Sunayana; Rathore G.S.

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Journal Paper

Paper Information

Journal: SAHAND COMMUNICATIONS IN MATHEMATICAL ANALYSIS (SCMA) Year:2020 | Volume:17 | Issue:2 Page(s): 185-201

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Information Journal Paper

Title

Generalized Continuous Frames for Operators

Author(s)

Shekhar Chander | Bhati Sunayana | Rathore G.S. | Issue Writer Certificate

Keywords

Frames

K-frames

Continuous frames

Abstract

In this note, the notion of generalized continuous K- frame in a Hilbert space is defined. Examples have been given to exhibit the existence of generalized continuous $K$-Frames. A necessary and sufficient condition for the existence of a generalized continuous $K$-frame in terms of its frame operator is obtained and a characterization of a generalized continuous $K$-frame for $ \mathcal{H} $ with respect to $ \mu $ is given. Also, a sufficient condition for a generalized continuous $K$-frame is given. Further, among other results, we prove that generalized continuous $K$-Frames are invariant under a linear homeomorphism. Finally, keeping in mind the importance of perturbation theory in various branches of applied mathematics, we study perturbation of $K$-Frames and obtain conditions for the stability of generalized continuous $K$-Frames.

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