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Generalized Weaving Frames for Operators in Hilbert Spaces

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Abstract

This paper studies weaving properties of a family of operators which are analysis and synthesis systems with frame-like properties for closed subspaces of a separable Hilbert space \(\mathcal {H}\), where the lower frame condition is controlled by a bounded operator on \(\mathcal {H}\). In short, this family of operators is called a \(\Theta \)-g-frame, where \(\Theta \) is a bounded operator on \(\mathcal {H}\). We present sufficient conditions for weaving \(\Theta \)-g-frames in separable Hilbert spaces. A characterization of weaving \(\Theta \)-g-frames in terms of an operator is given. It is shown that if frame bounds of frames associated with atomic spaces are positively confined, then \(\Theta \)-g-woven frames gives ordinary weaving \(\Theta \)-frames and vice-versa. We provide classes of operators for weaving \(\Theta \)-g-frames.

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Authors and Affiliations

  1. Department of Mathematics, University of Delhi, Delhi, 110007, India

    Deepshikha & Lalit K. Vashisht

  2. Centre for Industrial and Applied Mathematics, School of Information Technology and Mathematical Sciences, University of South Australia, Adelaide, Australia

    Geetika Verma

Authors
  1. Deepshikha
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  2. Lalit K. Vashisht
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  3. Geetika Verma
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Correspondence to Deepshikha.

Additional information

The first author is supported by CSIR, India, Grant No. 09/045(1352)/2014-EMR-I. Lalit was partially supported by R&D Doctoral Research Programme, University of Delhi, Delhi-110007, India (Grant No. RC/2015/9677).

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Deepshikha, Vashisht, L.K. & Verma, G. Generalized Weaving Frames for Operators in Hilbert Spaces. Results Math 72, 1369–1391 (2017). https://doi.org/10.1007/s00025-017-0704-6

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