Acta mathematica scientia, Series B >
INVERTIBLE SEQUENCES OF BOUNDED LINEAR OPERATORS
Received date: 2009-11-23
Revised date: 2010-08-26
Online published: 2011-09-20
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).
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
ZANG Li-Li , SUN Wen-Chang . INVERTIBLE SEQUENCES OF BOUNDED LINEAR OPERATORS[J]. Acta mathematica scientia, Series B, 2011 , 31(5) : 1939 -1944 . DOI: 10.1016/S0252-9602(11)60372-X
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