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Operator Frames for Banach Spaces

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Abstract

In this paper, operator Bessel sequences, operator frames, Banach operator frames, Operator Riesz bases for Banach spaces and dual frames of an operator frame are introduced and discussed. The necessary and sufficient condition for a Banach space to have an operator frame, a Banach operator frame or an operator Riesz basis are given. In addition, operator frames and operator Riesz bases are characterized by the analysis operator of operator Bessel sequences.

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Authors and Affiliations

  1. Department of Mathematics and Physics, Chongqing University of Science and Technology, Chongqing, 401331, People’s Republic of China

    Chun-Yan Li

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  1. Chun-Yan Li
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Correspondence to Chun-Yan Li.

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Communicated by Palle Jorgensen.

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Li, CY. Operator Frames for Banach Spaces. Complex Anal. Oper. Theory 6, 1–21 (2012). https://doi.org/10.1007/s11785-010-0076-3

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  • DOI: https://doi.org/10.1007/s11785-010-0076-3

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