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DOI: 10.46698/o3961-3328-9819-i

On Stability of Retro Banach Frame with Respect to \(b\)-Linear Functional in \(n\)-Banach Space

Ghosh, P.  , Samanta, T. K.
Vladikavkaz Mathematical Journal 2023. Vol. 25. Issue 1.
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.
Keywords: frame, Banach frame, retro Banach frame, stability, \(n\)-Banach space, \(b\)-linear functional
Language: English Download the full text  
For citation: Ghosh, P. and Samanta, T. K. On Stability of Retro Banach Frame with Respect to \(b\)-Linear Functional in \(n\)-Banach Space, Vladikavkaz Math. J., 2023, vol. 25, no. 1, pp. 48-63. DOI 10.46698/o3961-3328-9819-i
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