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On Some New Inequalities For Continuous Fusion Frames in Hilbert Spaces

  • Dongwei LiEmail author
  • Jinsong Leng
Article

Abstract

Continuous frames and fusion frames were considered recently as generalizations of frames in Hilbert spaces. In this paper, for any continuous fusion frame, we obtain a new family of inequalities which are parametrized by a parameter \(\lambda \in \mathbb {R}\). By suitable choices of \(\lambda \), one obtains the previous results as special cases. Moreover, these new inequalities involve the expressions \(\langle S_Yh,h \rangle \), \(\Vert S_Yh\Vert \), etc., where \(S_Y\) is a “truncated form” of the continuous fusion frame operator.

Keywords

Continuous fusion frames fusion frames dual frames operators 

Mathematics Subject Classification

Primary 42C15 Secondary 46C07 

Notes

Acknowledgements

The authors would like to thank the reviewer for several helpful suggestions that helped improve the presentation of this paper.

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of MathematicsHeFei University of TechnologyHefeiPeople’s Republic of China
  2. 2.School of Mathematical SciencesUniversity of Electronic Science and Technology of ChinaChengduPeople’s Republic of China

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