JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2019, Vol. 54 ›› Issue (8): 76-80.doi: 10.6040/j.issn.1671-9352.0.2018.724

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On decompositions of continuous generalized frames in Hilbert spaces

ZHANG Wei1, FU Yan-ling2   

  1. 1. School of Mathematics and Information Sciences, Henan University of Economics and Law, Zhengzhou 450046, Henan, China;
    2. Department of Information Engineering, Henan Finance University, Zhengzhou 451464, Henan, China
  • Online:2019-08-20 Published:2019-07-03

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Abstract: This paper establishes the characterization of continuous generalized frames,Parseval continuous g-frames,continuous generalized Riesz bases and continuous generalized orthonormal bases in term of the continuous generalized preframe operator. Using the established characterization results and decompositions of bounded operators, the representation of continuous generalized frames in term of linear combinations of simpler ones such as continuous generalized orthonormal bases, continuous generalized Riesz bases and Parseval continuous generalized frames is studied.

Key words: generalized frame, continuous generalized frame, continuous generalized orthonormal base, operator

CLC Number: 

  • O174.2
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