Geodesic
A note on fusion Banach frames
Archivum mathematicum, Tome 46 (2010) no. 3, pp. 203-209
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

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.
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.
Classification : 42A38, 42C15, 46B15
Keywords: atomic decompositions; fusion Banach frames; fusion bi-Banach frames 
@article{ARM_2010_46_3_a3,
     author = {Kaushik, S. K. and Kumar, Varinder},
     title = {A note on fusion {Banach} frames},
     journal = {Archivum mathematicum},
     pages = {203--209},
     year = {2010},
     volume = {46},
     number = {3},
     mrnumber = {2735906},
     zbl = {1240.42146},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ARM_2010_46_3_a3/}
}
TY  - JOUR
AU  - Kaushik, S. K.
AU  - Kumar, Varinder
TI  - A note on fusion Banach frames
JO  - Archivum mathematicum
PY  - 2010
SP  - 203
EP  - 209
VL  - 46
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/ARM_2010_46_3_a3/
LA  - en
ID  - ARM_2010_46_3_a3
ER  - 
%0 Journal Article
%A Kaushik, S. K.
%A Kumar, Varinder
%T A note on fusion Banach frames
%J Archivum mathematicum
%D 2010
%P 203-209
%V 46
%N 3
%U http://geodesic.mathdoc.fr/item/ARM_2010_46_3_a3/
%G en
%F ARM_2010_46_3_a3
Kaushik, S. K.; Kumar, Varinder. A note on fusion Banach frames. Archivum mathematicum, Tome 46 (2010) no. 3, pp. 203-209. http://geodesic.mathdoc.fr/item/ARM_2010_46_3_a3/

[1] Benedetto, J. J., Fickus, M.: Finite normalized tight frames. Adv. Comput. Math. 18 (2–4) (2003), 357–385. | DOI | MR | Zbl

[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. | MR | Zbl

[3] Christensen, O.: An Introduction to Frames and Reisz Bases. Birkhäuser, 2002.

[4] Daubechies, I., Grossmann, A., Meyer, Y.: Painless non-orthogonal expansions. J. Math. Phys. 27 (1986), 1271–1283. | DOI | MR

[5] Duffin, R. J., Schaeffer, A. C.: A class of non-harmonic Fourier Series. Trans. Amer. Math. Soc. 72 (1952), 341–366. | DOI | MR

[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. | MR

[7] Gröchenig, K.: Describing functions: Atomic decompositions versus frames. Monatsh. Math. 112 (1991), 1–41. | DOI | MR

[8] Jain, P. K., Kaushik, S. K., Gupta, N.: On near exact Banach frames in Banach spaces. Bull. Austral. Math. Soc. 78 (2008), 335–342. | DOI | MR | Zbl

[9] Jain, P. K., Kaushik, S. K., Kumar, V.: Frames of subspaces for Banach spaces. Int. J. Wavelets Multiresolut. Inf. Process. 8 (2) (2010), 243–252. | DOI | MR

[10] Jain, P. K., Kaushik, S. K., Vashisht, L. K.: Banach frames for conjugate Banach spaces. Z. Anal. Anwendungen 23 (4) (2004), 713–720. | DOI | MR | Zbl

[11] Jain, P. K., Kaushik, S. K., Vashisht, L. K.: On Banach frames. Indian J. Pure Appl. Math. 37 (5) (2006), 265–272. | MR | Zbl