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Approximation of the Inverse Frame Operator and Stability of Hilbert–Schmidt Frames

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Abstract

In this paper, we study the Hilbert–Schmidt frame (HS-frame) theory for separable Hilbert spaces. We first present some characterizations of HS-frames and prove that HS-frames share many important properties with frames. Then, we show how the inverse of the HS-frame operator can be approximated using finite-dimensional methods. Finally, we present a classical perturbation result and prove that HS-frames are stable under small perturbations.

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  1. Department of Mathematics, Indian Institute of Technology Guwahati, Guwahati, Assam , 781039, India

    Anirudha Poria

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  1. Anirudha Poria
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Poria, A. Approximation of the Inverse Frame Operator and Stability of Hilbert–Schmidt Frames. Mediterr. J. Math. 14, 153 (2017). https://doi.org/10.1007/s00009-017-0956-0

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  • DOI: https://doi.org/10.1007/s00009-017-0956-0

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