JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2024, Vol. 59 ›› Issue (4): 73-80.doi: 10.6040/j.issn.1671-9352.0.2022.468

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ε-approximations of continuous generalized frames

Wei ZHANG()   

  1. School of Mathematics and Information Sciences, Henan University of Economics and Law, Zhengzhou 450046, Henan, China
  • Received:2022-09-07 Online:2024-04-20 Published:2024-04-12

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Abstract:

This paper addresses the continuous generalized frame theory in Hilbert spaces. We introduce the concepts of ε-approximation, ε-closeness of continuous generalized frames, and establish a link between ε-approximation and ε-closeness. We present that the ε-approximations of continuous generalized frames are continuous generalized frames under certain conditions. Interestingly, the ε-approximations of tight continuous generalized frames can not be tight continuous generalized frames. Given a dual frame and ε-closeness of a continuous generalized frame, one can find a dual continuous generalized frame of its ε-closeness that makes the two dual continuous generalized frames close to each other.

Key words: continuous generalized frames, dual continuous generalized frames, ε-approximation

CLC Number: 

  • O174.2
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