On stability of retro Banach frame with respect to $b$-linear functional in $n$-Banach space
Vladikavkazskij matematičeskij žurnal, Tome 25 (2023) no. 1, pp. 48-63
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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.
@article{VMJ_2023_25_1_a3,
author = {P. Ghosh and T. K. Samanta},
title = {On stability of retro {Banach} frame with respect to $b$-linear functional in $n${-Banach} space},
journal = {Vladikavkazskij matemati\v{c}eskij \v{z}urnal},
pages = {48--63},
publisher = {mathdoc},
volume = {25},
number = {1},
year = {2023},
language = {en},
url = {http://geodesic.mathdoc.fr/item/VMJ_2023_25_1_a3/}
}
TY - JOUR AU - P. Ghosh AU - T. K. Samanta TI - On stability of retro Banach frame with respect to $b$-linear functional in $n$-Banach space JO - Vladikavkazskij matematičeskij žurnal PY - 2023 SP - 48 EP - 63 VL - 25 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/VMJ_2023_25_1_a3/ LA - en ID - VMJ_2023_25_1_a3 ER -
%0 Journal Article %A P. Ghosh %A T. K. Samanta %T On stability of retro Banach frame with respect to $b$-linear functional in $n$-Banach space %J Vladikavkazskij matematičeskij žurnal %D 2023 %P 48-63 %V 25 %N 1 %I mathdoc %U http://geodesic.mathdoc.fr/item/VMJ_2023_25_1_a3/ %G en %F VMJ_2023_25_1_a3
P. Ghosh; T. K. Samanta. On stability of retro Banach frame with respect to $b$-linear functional in $n$-Banach space. Vladikavkazskij matematičeskij žurnal, Tome 25 (2023) no. 1, pp. 48-63. http://geodesic.mathdoc.fr/item/VMJ_2023_25_1_a3/