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Applicable Analysis
An International Journal
Volume 100, 2021 - Issue 6
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Articles

On R-duals and the duality principle in Banach frames

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Pages 1256-1271 | Received 30 Nov 2018, Accepted 29 Jun 2019, Published online: 09 Jul 2019

References

  • Casazza PG, Dilworth SJ, Odell E, et al. Coefficient quantization for frames in Banach spaces. J Math Anal Appl. 2008;348:66–86. doi: 10.1016/j.jmaa.2008.06.055
  • Casazza PG, Han D, Larson D. Frames for Banach spaces. Contemp Math. 1999;247:149–182. doi: 10.1090/conm/247/03801
  • Casazza PG, Kutyniok G, Lammers MC. Duality principles in frame theory. J Fourier Anal Appl. 2004;10:383–408. doi: 10.1007/s00041-004-3024-7
  • Christensen O, Xiao XC, Zhu YC. Characterizing R-duality in Banach spaces. Acta Math Sin. 2013;29(1):75–84. doi: 10.1007/s10114-012-1199-4
  • Enayati F, Asgari MS. Duality properties for generalized frames. Banach J Math Anal. 2017;11(4):880–898. doi: 10.1215/17358787-2017-0027
  • Osgooei E, Najati A, Faroughi MH. G-Riesz dual sequences for g-Bessel sequences. Asian-Europ J Math. 2014;7:1450041. doi: 10.1142/S1793557114500417
  • Takhteh F, KHosravi A. R-duality in g-framesn. Rocky Mountain J Math. 2017;47(2):649–665. doi: 10.1216/RMJ-2017-47-2-649
  • Xiao XM, Zhu YC. Duality principles of frames in Banach spaces. Acta Math Sci Ser A Chin Ed. 2009;29:94–102.
  • Stoeva DT. Xd-Riesz bases in separable Banach spaces, Collection of papers, ded. to the 60th Anniv. of M. Konstantinov, BAS Publ. House; 2008.
  • Singer I. Bases in Banach spaces-II. Berlin-Heidelberg, New York: Springer Verlag; 1981.
  • Heil C. A basis theory primer. New York: Birkhäuser; 2011.
  • Christensen O, Heil C. Perturbations of Banach frames and atomic decompositions. Math Nachr. 1997;185:33–47. doi: 10.1002/mana.3211850104
  • Christensen O, Stoeva DT. P-frames in separable Banach spaces. Adv Comput Math. 2003;18:117–126. doi: 10.1023/A:1021364413257
  • Zhu YC. The stability of q-frames and p-Riesz bases in Banach spaces. Chin Ann Math. 2001;A22:359–364.
  • Casazza PG, Christensen O. Perturbation of operators and applications to frame theory. J Fourier Anal Appl. 1997;3:543–557. doi: 10.1007/BF02648883

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