-Operator frames for a Banach space |
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Authors: | Huai-Xin Cao Lan Li Qing-Jiang Chen Guo-Xing Ji |
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Institution: | aCollege of Mathematics and Information Science, Shaanxi Normal University, Xi'an 710062, China;bFaculty of Science, Xi'an Jiaotong University, Xi'an 710049, China |
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Abstract: | In this paper, (p,Y)-Bessel operator sequences, operator frames and (p,Y)-Riesz bases for a Banach space X are introduced and discussed as generalizations of the usual concepts for a Hilbert space and of the g-frames. It is proved that the set of all (p,Y)-Bessel operator sequences for a Banach space X is a Banach space and isometrically isomorphic to the operator space B(X,ℓp(Y)). Some necessary and sufficient conditions for a sequence of operators to be a (p,Y)-Bessel operator sequence are given. Also, a characterization of an independent (p,Y)-operator frame for X is obtained. Lastly, it is shown that an independent (p,Y)-operator frame for X is just a (p,Y)-Riesz basis for X and has a unique dual (q,Y*)-operator frame for X*. |
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Keywords: | (p Y)-Bessel operator sequence (p Y)-Operator frame (p Y)-Riesz basis Banach space |
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