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Characterizations of Disjointness of \(g\)-Frames and Constructions of \(g\)-Frames in Hilbert Spaces

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Abstract

Disjointness of frames in Hilbert spaces is closely related with superframes in Hilbert spaces and it also plays an important role in construction of superframes and frames, which were introduced and studied by Han and Larson. \(G\)-frame is a generalization of frame in Hilbert spaces, which covers many recent generalizations of frame in Hilbert spaces. In this paper, we study the \(g\)-frames in Hilbert spaces. We focus on the characterizations of disjointness of \(g\)-frames and constructions of \(g\)-frames. All types of disjointness are firstly characterized in terms of disjointness of frames induced by \(g\)-frames, then are characterized in terms of certain orthogonal projections. Finally we use disjoint \(g\)-frames to construct \(g\)-frames.

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Authors and Affiliations

  1. Department of Mathematics, Southwestern University of Finance and Economics, Chengdu, 611130, People’s Republic of China

    Xunxiang Guo

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  1. Xunxiang Guo
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Correspondence to Xunxiang Guo.

Additional information

Communicated by Palle Jorgensen.

This work was partially supported by SWUFE’s Key Subjects Construction Items Funds of 211 Project.

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Guo, X. Characterizations of Disjointness of \(g\)-Frames and Constructions of \(g\)-Frames in Hilbert Spaces. Complex Anal. Oper. Theory 8, 1547–1563 (2014). https://doi.org/10.1007/s11785-014-0364-4

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  • DOI: https://doi.org/10.1007/s11785-014-0364-4

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