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On perturbation of weighted \(g-\)Banach frames in Banach spaces. (English) Zbl 1463.42081

Summary: In the present paper, we study perturbation of weighted \(g-\)Banach frames in Banach spaces and obtain perturbation results for weighted \(g-\)Banach frames. Also, sufficient conditions for the perturbation of weighted \(g-\)Banach frames by positively confined sequence of scalars and uniformly scaled version of a given weighted \(g-\)Banach Bessel sequence have been given. Finally, we give a condition under which the sum of finite number of sequences of operators is a weighted \(g-\)Banach frame by comparing each of the sequences with another system of weighted \(g-\)Banach frames in Banach spaces.

MSC:

42C15 General harmonic expansions, frames
42A38 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
46B15 Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces
41A58 Series expansions (e.g., Taylor, Lidstone series, but not Fourier series)
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