Skip to main content
SpringerLink
Log in

Fusion Frames for Operators in Hilbert C*-Modules

  • Published:
Indian Journal of Pure and Applied Mathematics Aims and scope Submit manuscript

Abstract

In this paper we introduce K-fusion frames on a Hilbert C* -module H, where K is an adjointable operator on H. We obtain several characterizations of K-fusion frames. In addition, we extend the concept of duality to K-fusion frames and study some of its properties.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. A. Alijani and M. A. Dehghan, ’G-Frames and Their Duals in Hilbert C* -Modules’, Bull. Iranian Math. Soc., 38 (2012), 567–580.

    MathSciNet  MATH  Google Scholar 

  2. I. Daubechies, A. Grossmann, and Y. Meyer, Painless Nonorthogonal Expansions, J. Math. Phys., 27: (1986), 1271–1283.

    Article  MathSciNet  Google Scholar 

  3. R. J. Duffin and A. C. Schaeffer, A class of nonharmonic fourier series, Trans. Amer. Math. Soc., 72 (1952), 341–366.

    Article  MathSciNet  Google Scholar 

  4. X. C. Fang, J. Yu, and H. L. Yao, Solutions to Operator Equations on Hilbert C* -Modules, Linear Algebra Appl., 431 (2009), 2142–2153.

    Article  MathSciNet  Google Scholar 

  5. H. G. Feichtinger and T. Werther, Atomic Systems for Subspaces In: Zayed AI, editor. Proceedings of the 2001 International Conference on Sampling Theory and Applications, 13–17 May 2001, Orlando, FL, USA. New York: IEEE, pp. 163–165, 2001.

  6. M. Frank and D. R. Larson, Frames in Hilbert C* -modules and C* -algebras, J. Operator Theory, 48 (2002), 273–314.

    MathSciNet  MATH  Google Scholar 

  7. L. Gavruta, Frames for operators, Appl. Comput. Harmon. Anal., 32 (2012), 139–144.

    Article  MathSciNet  Google Scholar 

  8. S. B. Heineken, P. M. Morillas, A. M. Benavente, and M. I. Zakowicz, Dual Fusion Frames, Arch. Math., 103 (2014), 355–365.

    Google Scholar 

  9. S. Heineken and P. Morillas, Properties of finite dual fusion frames, Linear Algebra and Its Applications, 453 (2014), 1–27.

    Article  MathSciNet  Google Scholar 

  10. W. Jing, Frames in Hilbert C* -modules PhD, University of Central Florida, Orlando. FL, USA, 2006.

  11. A. Khosravi and B. Khosravi, Fusion frames and g-frames in Hilbert C*-modules, Int. J. Wavelets Multiresolut Inf. Process, 6: (2008), 433–446.

    Article  MathSciNet  Google Scholar 

  12. E. C. Lance, Hilbert C* -modules — A toolkit for operator algebraist, London Math. Soc. Lecture Note Ser., Volume 210, Cambridge, UK: Cambridge University Press, 1995.

    Google Scholar 

  13. A. Najati, M. M. Seam, and P. Gavrute, Frames and operators in Hilbert C*-modules, ❬www.arxiv.org❭., math. OA/1403.0204vl.

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Kerman Branch, Islamic Azad University, Kerman, Iran

    M. Khayyami

  2. Department of Pure Mathematics Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran, 76169-14111

    A. Nazari

Authors
  1. M. Khayyami
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. Nazari
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to M. Khayyami or A. Nazari.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Khayyami, M., Nazari, A. Fusion Frames for Operators in Hilbert C*-Modules. Indian J Pure Appl Math 51, 791–803 (2020). https://doi.org/10.1007/s13226-020-0432-6

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13226-020-0432-6

Key words

2010 Mathematics Subject Classification

Search

Navigation