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On stability of retro Banach frame with respect to $b$-linear functional in $n$-Banach space
P. Ghosha, T. K. Samantab a Department of Pure Mathematics, University of Calcutta, 35 Ballygunge Circular Road, Kolkata 700019, West Bengal, India
b Department of Mathematics, Uluberia College, Uluberia, Howrah 711315, West Bengal, India
Abstract:
We introduce the notion of a retro Banach frame relative to a bounded $b$-linear functional in $n$-Banach space and see that the sum of two retro Banach frames in $n$-Banach space with different reconstructions operators is also a retro Banach frame in $n$-Banach space. Also, we define retro Banach Bessel sequence with respect to a bounded $b$-linear functional in $n$-Banach space. A necessary and sufficient condition for the stability of retro Banach frame with respect to bounded $b$-linear functional in $n$-Banach space is being obtained. Further, we prove that retro Banach frame with respect to bounded $b$-linear functional in $n$-Banach space is stable under perturbation of frame elements by positively confined sequence of scalars. In $n$-Banach space, some perturbation results of retro Banach frame with the help of bounded $b$-linear functional in $n$-Banach space have been studied. Finally, we give a sufficient condition for finite sum of retro Banach frames to be a retro Banach frame in $n$-Banach space. At the end, we discuss retro Banach frame with respect to a bounded $b$-linear functional in Cartesian product of two $n$-Banach spaces.
Key words:
frame, Banach frame, retro Banach frame, stability, $n$-Banach space, $b$-linear functional.
Received: 09.11.2021
Citation:
P. Ghosh, T. K. Samanta, “On stability of retro Banach frame with respect to $b$-linear functional in $n$-Banach space”, Vladikavkaz. Mat. Zh., 25:1 (2023), 48–63
Linking options:
https://www.mathnet.ru/eng/vmj847 https://www.mathnet.ru/eng/vmj/v25/i1/p48
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Abstract page: | 61 | Full-text PDF : | 28 | References: | 21 |
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