| Title:
|
On the existence of non-linear frames (English) |
| Author:
|
Jahan, Shah |
| Author:
|
Kumar, Varinder |
| Author:
|
Kaushik, S.K. |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
53 |
| Issue:
|
2 |
| Year:
|
2017 |
| Pages:
|
101-109 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
Banach frames |
| Keyword:
|
retro Banach frames |
| Keyword:
|
approximative Schauder frames |
| MSC:
|
42C15 |
| MSC:
|
46B15 |
| idZBL:
|
Zbl 06770055 |
| idMR:
|
MR3672784 |
| DOI:
|
10.5817/AM2017-2-101 |
| . |
| Date available:
|
2017-06-09T07:51:19Z |
| Last updated:
|
2020-01-05 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/146797 |
| . |
| Reference:
|
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