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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