On the existence of non-linear frames

Shah Jahan; Varinder Kumar; S.K. Kaushik

Archivum Mathematicum (2017)

  • Volume: 053, Issue: 2, page 101-109
  • ISSN: 0044-8753

Abstract

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A stronger version of the notion of frame in Banach space called Strong Retro Banach frame (SRBF) is defined and studied. It has been proved that if 𝒳 is a Banach space such that 𝒳 * has a SRBF, then 𝒳 has a Bi-Banach frame with some geometric property. Also, it has been proved that if a Banach space 𝒳 has an approximative Schauder frame, then 𝒳 * has a SRBF. Finally, the existence of a non-linear SRBF in the conjugate of a separable Banach space has been proved.

How to cite

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Jahan, Shah, Kumar, Varinder, and Kaushik, S.K.. "On the existence of non-linear frames." Archivum Mathematicum 053.2 (2017): 101-109. <http://eudml.org/doc/288212>.

@article{Jahan2017,
abstract = {A stronger version of the notion of frame in Banach space called Strong Retro Banach frame (SRBF) is defined and studied. It has been proved that if $\mathcal \{X\}$ is a Banach space such that $\mathcal \{X^*\}$ has a SRBF, then $\mathcal \{X\}$ has a Bi-Banach frame with some geometric property. Also, it has been proved that if a Banach space $\mathcal \{X\}$ has an approximative Schauder frame, then $\mathcal \{X^*\}$ has a SRBF. Finally, the existence of a non-linear SRBF in the conjugate of a separable Banach space has been proved.},
author = {Jahan, Shah, Kumar, Varinder, Kaushik, S.K.},
journal = {Archivum Mathematicum},
keywords = {Banach frames; retro Banach frames; approximative Schauder frames},
language = {eng},
number = {2},
pages = {101-109},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {On the existence of non-linear frames},
url = {http://eudml.org/doc/288212},
volume = {053},
year = {2017},
}

TY - JOUR
AU - Jahan, Shah
AU - Kumar, Varinder
AU - Kaushik, S.K.
TI - On the existence of non-linear frames
JO - Archivum Mathematicum
PY - 2017
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 053
IS - 2
SP - 101
EP - 109
AB - A stronger version of the notion of frame in Banach space called Strong Retro Banach frame (SRBF) is defined and studied. It has been proved that if $\mathcal {X}$ is a Banach space such that $\mathcal {X^*}$ has a SRBF, then $\mathcal {X}$ has a Bi-Banach frame with some geometric property. Also, it has been proved that if a Banach space $\mathcal {X}$ has an approximative Schauder frame, then $\mathcal {X^*}$ has a SRBF. Finally, the existence of a non-linear SRBF in the conjugate of a separable Banach space has been proved.
LA - eng
KW - Banach frames; retro Banach frames; approximative Schauder frames
UR - http://eudml.org/doc/288212
ER -

References

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