On stability of retro Banach frame with respect to b-linear functional in n-Banach space
Автор: Ghosh Prasenjit, Samanta Tapas Kumar
Журнал: Владикавказский математический журнал @vmj-ru
Статья в выпуске: 1 т.25, 2023 года.
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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.
Frame, banach frame, retro banach frame, stability, n-banach space, b-linear functional
Короткий адрес: https://sciup.org/143179838
IDR: 143179838 | DOI: 10.46698/o3961-3328-9819-i
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