数学物理学报(英文版) ›› 2011, Vol. 31 ›› Issue (5): 1939-1944.doi: 10.1016/S0252-9602(11)60372-X

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INVERTIBLE SEQUENCES OF BOUNDED LINEAR OPERATORS

臧丽丽|孙文昌*   

  1. Department of Mathematics and LPMC, Nankai University, Tianjin 300071, China
  • 收稿日期:2009-11-23 修回日期:2010-08-26 出版日期:2011-09-20 发布日期:2011-09-20
  • 通讯作者: 孙文昌,sunwch@nankai.edu.cn E-mail:zanglili@mail.nankai.edu.cn; sunwch@nankai.edu.cn
  • 基金资助:

    This work was supported partially by the National Natural Science Foundation of China (10971105 and 10990012) and the Natural Science Foundation of Tianjin (09JCYBJC01000).

INVERTIBLE SEQUENCES OF BOUNDED LINEAR OPERATORS

 ZANG Li-Li, SUN Wen-Chang*   

  1. Department of Mathematics and LPMC, Nankai University, Tianjin 300071, China
  • Received:2009-11-23 Revised:2010-08-26 Online:2011-09-20 Published:2011-09-20
  • Contact: SUN Wen-Chang,sunwch@nankai.edu.cn E-mail:zanglili@mail.nankai.edu.cn; sunwch@nankai.edu.cn
  • Supported by:

    This work was supported partially by the National Natural Science Foundation of China (10971105 and 10990012) and the Natural Science Foundation of Tianjin (09JCYBJC01000).

摘要:

In this paper, we study the invertibility of sequences consisting of finitely many bounded linear operators from a Hilbert space to others. We show that a sequence of operators is left invertible if and only if it is a g-frame. Therefore, our result connects the invertibility of operator sequences with frame theory.

关键词: frames, g-frames, Riesz bases, g-Riesz bases

Abstract:

In this paper, we study the invertibility of sequences consisting of finitely many bounded linear operators from a Hilbert space to others. We show that a sequence of operators is left invertible if and only if it is a g-frame. Therefore, our result connects the invertibility of operator sequences with frame theory.

Key words: frames, g-frames, Riesz bases, g-Riesz bases

中图分类号: 

  • 46C05