A note on fusion Banach frames

S. K. Kaushik; Varinder Kumar

Archivum Mathematicum (2010)

  • Volume: 046, Issue: 3, page 203-209
  • ISSN: 0044-8753

Abstract

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For a fusion Banach frame ( { G n , v n } , S ) for a Banach space E , if ( { v n * ( E * ) , v n * } , T ) is a fusion Banach frame for E * , then ( { G n , v n } , S ; { v n * ( E * ) , v n * } , T ) is called a fusion bi-Banach frame for E . It is proved that if E has an atomic decomposition, then E also has a fusion bi-Banach frame. Also, a sufficient condition for the existence of a fusion bi-Banach frame is given. Finally, a characterization of fusion bi-Banach frames is given.

How to cite

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Kaushik, S. K., and Kumar, Varinder. "A note on fusion Banach frames." Archivum Mathematicum 046.3 (2010): 203-209. <http://eudml.org/doc/116483>.

@article{Kaushik2010,
abstract = {For a fusion Banach frame $(\lbrace G_n, v_n\rbrace , S)$ for a Banach space $E$, if $(\lbrace v_n^*(E^*), v_n^*\rbrace ,T)$ is a fusion Banach frame for $E^*$, then $(\lbrace G_n, v_n\rbrace , S; \lbrace v_n^*(E^*), v_n^*\rbrace ,T)$ is called a fusion bi-Banach frame for $E$. It is proved that if $E$ has an atomic decomposition, then $E$ also has a fusion bi-Banach frame. Also, a sufficient condition for the existence of a fusion bi-Banach frame is given. Finally, a characterization of fusion bi-Banach frames is given.},
author = {Kaushik, S. K., Kumar, Varinder},
journal = {Archivum Mathematicum},
keywords = {atomic decompositions; fusion Banach frames; fusion bi-Banach frames; atomic decomposition; fusion Banach frame; fusion bi-Banach frame},
language = {eng},
number = {3},
pages = {203-209},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {A note on fusion Banach frames},
url = {http://eudml.org/doc/116483},
volume = {046},
year = {2010},
}

TY - JOUR
AU - Kaushik, S. K.
AU - Kumar, Varinder
TI - A note on fusion Banach frames
JO - Archivum Mathematicum
PY - 2010
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 046
IS - 3
SP - 203
EP - 209
AB - For a fusion Banach frame $(\lbrace G_n, v_n\rbrace , S)$ for a Banach space $E$, if $(\lbrace v_n^*(E^*), v_n^*\rbrace ,T)$ is a fusion Banach frame for $E^*$, then $(\lbrace G_n, v_n\rbrace , S; \lbrace v_n^*(E^*), v_n^*\rbrace ,T)$ is called a fusion bi-Banach frame for $E$. It is proved that if $E$ has an atomic decomposition, then $E$ also has a fusion bi-Banach frame. Also, a sufficient condition for the existence of a fusion bi-Banach frame is given. Finally, a characterization of fusion bi-Banach frames is given.
LA - eng
KW - atomic decompositions; fusion Banach frames; fusion bi-Banach frames; atomic decomposition; fusion Banach frame; fusion bi-Banach frame
UR - http://eudml.org/doc/116483
ER -

References

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  1. Benedetto, J. J., Fickus, M., 10.1023/A:1021323312367, Adv. Comput. Math. 18 (2–4) (2003), 357–385. (2003) Zbl1028.42022MR1968126DOI10.1023/A:1021323312367
  2. Casazza, P. G., Custom Building finite frames, Wavelets, Frames and Operator Theory (Heil, C., Jorgensen, P. E. T., Larson, D. R., eds.), vol. 345, Contemp. Math., 2004, pp. 81–86. (2004) Zbl1082.42024MR2066822
  3. Christensen, O., An Introduction to Frames and Reisz Bases, Birkhäuser, 2002. (2002) 
  4. Daubechies, I., Grossmann, A., Meyer, Y., 10.1063/1.527388, J. Math. Phys. 27 (1986), 1271–1283. (1986) MR0836025DOI10.1063/1.527388
  5. Duffin, R. J., Schaeffer, A. C., 10.1090/S0002-9947-1952-0047179-6, Trans. Amer. Math. Soc. 72 (1952), 341–366. (1952) MR0047179DOI10.1090/S0002-9947-1952-0047179-6
  6. Feichtinger, H. G., Gröchenig, K., A unified approach to atomic decompositons via integrable group representations, Proc. Conf. Function Spaces and Applications, Lecture Notes in Math. 1302, Berlin-Heidelberg-New York, Springer, 1988, pp. 52–73. (1988) MR0942257
  7. Gröchenig, K., 10.1007/BF01321715, Monatsh. Math. 112 (1991), 1–41. (1991) MR1122103DOI10.1007/BF01321715
  8. Jain, P. K., Kaushik, S. K., Gupta, N., 10.1017/S0004972708000889, Bull. Austral. Math. Soc. 78 (2008), 335–342. (2008) Zbl1214.42060MR2466869DOI10.1017/S0004972708000889
  9. Jain, P. K., Kaushik, S. K., Kumar, V., 10.1142/S0219691310003481, Int. J. Wavelets Multiresolut. Inf. Process. 8 (2) (2010), 243–252. (2010) MR2651164DOI10.1142/S0219691310003481
  10. Jain, P. K., Kaushik, S. K., Vashisht, L. K., 10.4171/ZAA/1217, Z. Anal. Anwendungen 23 (4) (2004), 713–720. (2004) Zbl1059.42024MR2110399DOI10.4171/ZAA/1217
  11. Jain, P. K., Kaushik, S. K., Vashisht, L. K., On Banach frames, Indian J. Pure Appl. Math. 37 (5) (2006), 265–272. (2006) Zbl1125.46013MR2271627

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