175
Views
0
CrossRef citations to date
0
Altmetric
Articles

Invertibility of g-frame multipliers and Bessel multipliers for unitary systems in Hilbert C*-modules

Pages 1663-1681 | Received 14 Oct 2018, Accepted 26 Nov 2018, Published online: 07 Dec 2018

References

  • Duffin RJ, Schaeffer AC. A class of nonharmonic Fourier series. Trans Amer Math Soc. 1952;72:341–366. doi: 10.1090/S0002-9947-1952-0047179-6
  • Bemrose T, Casazza PG, Gröchenig K, et al. Weaving frames. Oper Matrices. 2016;10:1093–1116. doi: 10.7153/oam-10-61
  • Benedetto J, Powell A, Yilmaz O. Sigma-Delta (ΣΔ) quantization and finite frames. IEEE Trans Inform Theory. 2006;52:1990–2005. doi: 10.1109/TIT.2006.872849
  • Casazza PG. The art of frame theory. Taiwanese J Math. 2000;4:129–201. doi: 10.11650/twjm/1500407227
  • Christensen O. An introduction to frames and Riesz bases. Boston (MA): Birkhäuser; 2000.
  • Christensen O, Hasannasab M. Operator representations of frames: boundedness, duality, and stability. Integral Equ Oper Theory. 2017;88:483–499. doi: 10.1007/s00020-017-2370-1
  • Christensen O, Hasannasab M, Rashidi E. Dynamical sampling and frame representations with bounded operators. J Math Anal Appl. 2018;463:634–644. doi: 10.1016/j.jmaa.2018.03.039
  • Daubechies I, Grossmann A, Meyer Y. Painless nonorthogonal expansions. J Math Phys. 1986;27:1271–1283. doi: 10.1063/1.527388
  • Han D, Sun W. Reconstruction of signals from frame coefficients with erasures at unknown locations. IEEE Trans Inform Theory. 2014;60:4013–4025. doi: 10.1109/TIT.2014.2320937
  • Strohmer T, Heath R. Grassmannian frames with applications to coding and communication. Appl Comput Harmon Anal. 2003;14:257–275. doi: 10.1016/S1063-5203(03)00023-X
  • Sun W. Asymptotic properties of Gabor frame operators as sampling density tends to infinity. J Funct Anal. 2010;258:913–932. doi: 10.1016/j.jfa.2009.09.018
  • Sun W. G-frames and g-Riesz bases. J Math Anal Appl. 2006;322:437–452. doi: 10.1016/j.jmaa.2005.09.039
  • Li JZ, Zhu YC. Exact g-frames in Hilbert spaces. J Math Anal Appl. 2011;374:201–209. doi: 10.1016/j.jmaa.2010.08.042
  • Sun W. Stability of g-frames. J Math Anal Appl. 2007;326:858–868. doi: 10.1016/j.jmaa.2006.03.043
  • Alijani A, Dehghan MA. G-frames and their duals for Hilbert C∗-modules. Bull Iranian Math Soc. 2012;38:567–580.
  • Alijani A. Generalized frames with C∗-valued bounds and their operator duals. Filomat. 2015;29:1469–1479. doi: 10.2298/FIL1507469A
  • Arambašić L. On frames for countably generated Hilbert C∗-modules. Proc Amer Math Soc. 2007;135:469–478. doi: 10.1090/S0002-9939-06-08498-X
  • Arambašić L, Bakić D. Frames and outer frames for Hilbert C∗-modules. Linear Multilinear Algebra. 2017;65:381–431. doi: 10.1080/03081087.2016.1186588
  • Frank M, Larson D. Frames in Hilbert C∗-modules and C∗-algebras. J Operator Theory. 2002;48:273–314.
  • Han D, Jing W, Larson D, et al. Dilation of dual frame pairs in Hilbert C∗-modules. Results Math. 2013;63:241–250. doi: 10.1007/s00025-011-0195-9
  • Khosravi A, Khosravi B. Fusion frames and g-frames in Hilbert C∗-modules. Int J Wavelets Multiresolut Inf Process. 2008;6:433–446. doi: 10.1142/S0219691308002458
  • Khosravi A, Khosravi B. G-frames and modular Riesz bases in Hilbert C∗-modules. Int J Wavelets Multiresolut Inf Process. 2012;10:1250013,12 pp. doi: 10.1142/S0219691312500130
  • Xiao XC, Zeng XM. Some properties of g-frames in Hilbert C∗-modules. J Math Anal Appl. 2010;363:399–408. doi: 10.1016/j.jmaa.2009.08.043
  • Balazs P. Basic definition and properties of Bessel multipliers. J Math Anal Appl. 2007;325:571–585. doi: 10.1016/j.jmaa.2006.02.012
  • Balazs P. Hilbert-Schmidt operators and frames-classification, best approximation by multipliers and algorithms. Int J Wavelets Multiresolut Inf Process. 2008;6:315–330. doi: 10.1142/S0219691308002379
  • Cordero E, Gröchenig K. Necessary conditions for Schatten class localization operators. Proc Amer Math Soc. 2005;133:3573–3579. doi: 10.1090/S0002-9939-05-07897-4
  • Cordero E, Gröchenig K, Nicola F. Approximation of Fourier integral operators by Gabor multipliers. J Fourier Anal Appl. 2012;18:661–684. doi: 10.1007/s00041-011-9214-1
  • Feichtinger HG, Hampejs M, Kracher G. Approximation of matrices by Gabor multipliers. IEEE Signal Process Lett. 2004;11:883–886. doi: 10.1109/LSP.2004.833581
  • Futamura F. Frame diagonalization of matrices. Linear Algebra Appl. 2012;436:3201–3214. doi: 10.1016/j.laa.2011.11.001
  • Gröchenig K. Representation and approximation of pseudo differential operators by sums of Gabor multipliers. Appl Anal. 2011;90:385–401. doi: 10.1080/00036811.2010.499507
  • Rahimi A. Multipliers of generalized frames in Hilbert spaces. Bull Iranian Math Soc. 2011;37:63–80.
  • Shamsabadi M, Arefijamaal AA. The invertibility of fusion frame multipliers. Linear Multilinear Algebra. 2017;65:1062–1072. doi: 10.1080/03081087.2016.1228803
  • Khosravi A, Mirzaee Azandaryani M. Bessel multipliers in Hilbert C∗-modoles. Banach J Math Anal. 2015;9:153–163. doi: 10.15352/bjma/09-3-11
  • Stoeva DT, Balazs P. Invertibility of multipliers. Appl Comput Harmon Anal. 2012;33:292–299. doi: 10.1016/j.acha.2011.11.001
  • Mirzaee Azandaryani M. Approximate duals and nearly Parseval frames. Turkish J Math. 2015;39:515–526. doi: 10.3906/mat-1408-37

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.