Generalized Fusion Frame in A Tensor Product of Hilbert Space

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Authors

  • Prasenjit Ghosh
     Department of Pure Mathematics, University of Calcutta, Kolkata, 700019 ,IN
  • T. K. Samanta
     Department of Mathematics, Uluberia College, Uluberia, Howrah, 711315 ,IN

DOI:

https://doi.org/10.18311/jims/2022/29307

Keywords:

Frame, fusion frame, g-frame, g-fusion frame, frame operator, Tensor product of Hilbert spaces, Tensor product of frames

Abstract

Generalized fusion frames and some of their properties in a tensor product of Hilbert spaces are studied. Also, the canonical dual g-fusion frame in a tensor product of Hilbert spaces is considered. The frame operator for a pair of g-fusion Bessel sequences in a tensor product of Hilbert spaces is presented.

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Published

2022-01-27

How to Cite

Ghosh, P., & Samanta, T. K. (2022). Generalized Fusion Frame in A Tensor Product of Hilbert Space. The Journal of the Indian Mathematical Society, 89(1-2), 58–71. https://doi.org/10.18311/jims/2022/29307

Issue

Volume 89, Issue 1-2, January-June 2022

Section

Articles

License

Copyright (c) 2022 Prasenjit Ghosh, T. K. Samanta

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

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Europe PMC
Received 2022-01-11
Accepted 2023-01-30
Published 2022-01-27

 

References

M. S. Asgari and A. Khosravi, Frames and bases of subspaces in Hilbert spaces, J. Math. Anal. Appl., 308 (2005) 541–553. DOI: https://doi.org/10.1016/j.jmaa.2004.11.036

P. Casazza and G. Kutyniok, Frames of subspaces, Cotemporary Math., AMS 345 (2004), 87–114. DOI: https://doi.org/10.1090/conm/345/06242

O. Christensen, An Introduction to Frames and Riesz Bases, Birkhauser, 2008.

R. J. Duffin and A. C. Schaeffer, A class of nonharmonic Fourier series, Trans. Amer. Math. Soc., 72, (1952), 341–366. DOI: https://doi.org/10.1090/S0002-9947-1952-0047179-6

G. B. Folland, A Course in Abstract Harmonic Analysis, CRC Press BOCA Raton, Florida, 1995.

P. Gavruta, On the duality of fusion frames, J. Math. Anal. Appl. 333 (2007), 871–879. DOI: https://doi.org/10.1016/j.jmaa.2006.11.052

P. Ghosh and T. K. Samanta, Stability of dual g-fusion frame in Hilbert spaces, Methods Funct. Anal. Topology, 26 (3) (2020), 227–240. DOI: https://doi.org/10.31392/MFAT-npu26_3.2020.04

P. Ghosh and T. K. Samanta, Generalized atomic subspaces for operators in Hilbert spaces, Math. Bohem., (Accepted), DOI: 10.21136/MB.2021.0130-20 DOI: https://doi.org/10.21136/MB.2021.0130-20

P. Ghosh and T. K. Samanta, Fusion frame and its alternative dual in tensor product of Hilbert spaces, arXiv:2105.03094.

Amir Khoravi and M. S. Asgari, Frames and Bases in Tensor Product of Hilbert spaces, Intern. Math. J., 4(6), (2003), 527–537.

Amir Khosravi and M. Mirzaee Azandaryani, Fusion frames and g-frames in tensor product and direct sum of Hilbert spaces, Appl. Anal. Discrete Math., 6 (2012), 287–303. DOI: https://doi.org/10.2298/AADM120619014K

S. Rabinson, Hilbert space and tensor products, Lecture notes, September 8, 1997.

V. Sadri, Gh. Rahimlou, R. Ahmadi and R. Zarghami Farfar, Generalized Fusion Frames in Hilbert Spaces, arXiv: 1806.03598v1, Submitted (2018).

W. Sun, G-frames and G-Riesz bases, J. Math. Anal. Appl. 322 (1) (2006), 437–452. DOI: https://doi.org/10.1016/j.jmaa.2005.09.039

G. Upender Reddy, N. Gopal Reddy and B. Krishna Reddy, Frame operator and Hilbert- Schmidt operator in tensor product of Hilbert spaces, J. Dynamical Systems and Geometric Theories, 7(1) (2009), 61–70. DOI: https://doi.org/10.1080/1726037X.2009.10698563