Acta mathematica scientia,Series B ›› 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

 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).

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

CLC Number: 

  • 46C05
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