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Volume 40, Issue 4
Toeplitz $O$-Frames for Operators in Banach Spaces

Chander Shekhar & S. K. Kaushik

DOI: 10.4208/ata.OA-2017-0028

Anal. Theory Appl., 40 (2024), pp. 363-373.

Published online: 2025-02

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  • Abstract

We define Toeplitz $O$-frame for operators as a generalization of the notion of $O$-frame introduced by Reinov [11]. A necessary condition for the existence of a Toeplitz $O$-frame is given. It has been proved that an $O$-frame for operators can generate a Toeplitz $O$-frame from a given Toeplitz matrix but the converse need not be true. Also, a sufficient condition on infinite matrices for the existence of an $O$-frame is given. Finally, the notion of a strong $O$-frame is defined and a necessary and sufficient condition for its existence has been obtained.

  • Keywords

Frames, operators, $O$-frames.

  • AMS Subject Headings

42C15, 46B28

  • Copyright

COPYRIGHT: © Global Science Press

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  • TXT
@Article{ATA-40-363, author = {Shekhar , Chander and Kaushik , S. K.}, title = {Toeplitz $O$-Frames for Operators in Banach Spaces}, journal = {Analysis in Theory and Applications}, year = {2025}, volume = {40}, number = {4}, pages = {363--373}, abstract = {

We define Toeplitz $O$-frame for operators as a generalization of the notion of $O$-frame introduced by Reinov [11]. A necessary condition for the existence of a Toeplitz $O$-frame is given. It has been proved that an $O$-frame for operators can generate a Toeplitz $O$-frame from a given Toeplitz matrix but the converse need not be true. Also, a sufficient condition on infinite matrices for the existence of an $O$-frame is given. Finally, the notion of a strong $O$-frame is defined and a necessary and sufficient condition for its existence has been obtained.

}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.OA-2017-0028}, url = {http://global-sci.org/intro/article_detail/ata/23859.html} }
TY - JOUR T1 - Toeplitz $O$-Frames for Operators in Banach Spaces AU - Shekhar , Chander AU - Kaushik , S. K. JO - Analysis in Theory and Applications VL - 4 SP - 363 EP - 373 PY - 2025 DA - 2025/02 SN - 40 DO - http://doi.org/10.4208/ata.OA-2017-0028 UR - https://global-sci.org/intro/article_detail/ata/23859.html KW - Frames, operators, $O$-frames. AB -

We define Toeplitz $O$-frame for operators as a generalization of the notion of $O$-frame introduced by Reinov [11]. A necessary condition for the existence of a Toeplitz $O$-frame is given. It has been proved that an $O$-frame for operators can generate a Toeplitz $O$-frame from a given Toeplitz matrix but the converse need not be true. Also, a sufficient condition on infinite matrices for the existence of an $O$-frame is given. Finally, the notion of a strong $O$-frame is defined and a necessary and sufficient condition for its existence has been obtained.

Shekhar , Chander and Kaushik , S. K.. (2025). Toeplitz $O$-Frames for Operators in Banach Spaces. Analysis in Theory and Applications. 40 (4). 363-373. doi:10.4208/ata.OA-2017-0028
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