Acta mathematica scientia,Series A ›› 2022, Vol. 42 ›› Issue (3): 694-704.

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Q-(Approximate) Dual of g-Frames in Hilbert Spaces

Wei Zhang1,*(),Yanling Fu2(),Shuanbao Li3()   

  1. 1 School of Mathematics and Information Sciences, Henan University of Economics and Law, Zhengzhou 450046
    2 School of Statistics and Mathematics, Henan Finance University, Zhengzhou 450046
    3 School of Artificial Intelligence, Henan Finance University, Zhengzhou 450046
  • Received:2021-05-19 Online:2022-06-26 Published:2022-05-09
  • Contact: Wei Zhang E-mail:zwfylhappy@126.com;jzhou111@163.com;phdfuli@whu.edu.cn
  • Supported by:
    the NSFC(11761079);the Key Scientific Research Projects of Colleges and Universities of Henan Province(20A110013);the Key Scientific Research Projects of Colleges and Universities of Henan Province(21A110004);the Science and Technology Research Project of Henan Province(182102210215);the Science and Technology Research Project of Henan Province(222102210335)

Abstract:

In this paper, fusing the ideas of dual Fusion frames and approximate dual g-frames, the definitions of Q-(approximate) dual g-frames are given. The relationship between Q-approximate dual g-frames and Q-dual g-frames is discussed. The characterizations of Q-(approximate) dual g-frames are obtained. Finally, by means of Q-approximate dual g-frames, some equivalent conditions for a g-frame to be close to another g-frame are given.

Key words: G-frame, Q-(approximate) dual g-frame, Closeness

CLC Number: 

  • O174.2
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