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Some Properties of K-Frames in Quaternionic Hilbert Spaces

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Abstract

In the present paper, we discuss some properties of K-frames in quaternionic Hilbert spaces such as the invertibility of the frame operator as well as the interchangeability of two Bessel sequences. Further, we propose several approaches to construct K-frames and we show that a T-frame can be constructed from a K-frame by the perturbation of a bounded linear operator T. Finally, we study the stability of K-frames under some perturbations.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Sciences of Sfax, BP 1171, 3000, Sfax, Tunisia

    Hanen Ellouz

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  1. Hanen Ellouz
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Correspondence to Hanen Ellouz.

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Communicated by Daniel Aron Alpay.

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This article is part of the topical collection “Spectral Theory and Operators in Mathematical Physics” edited by Jussi Behrndt, Fabrizio Colombo and Sergey Naboko.

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Ellouz, H. Some Properties of K-Frames in Quaternionic Hilbert Spaces. Complex Anal. Oper. Theory 14, 8 (2020). https://doi.org/10.1007/s11785-019-00964-5

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  • DOI: https://doi.org/10.1007/s11785-019-00964-5

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