Geodesic
On the existence of non-linear frames
Archivum mathematicum, Tome 53 (2017) no. 2, pp. 101-109
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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 $\mathcal{X}$ 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.
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.
DOI : 10.5817/AM2017-2-101
Classification : 42C15, 46B15
Keywords: Banach frames; retro Banach frames; approximative Schauder frames 
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Jahan, Shah; Kumar, Varinder; Kaushik, S.K. On the existence of non-linear frames. Archivum mathematicum, Tome 53 (2017) no. 2, pp. 101-109. doi: 10.5817/AM2017-2-101

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