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On Perturbation of Weighted G−Banach Frames in Banach Spaces


Affiliations
1 Department of Mathematics and Statistics, University College of Science, M.L.S. University, Udaipur, India
2 Department of Mathematics, Dr. Akhilesh Das Gupta, Institute of Technology and Management, G.G.S. Inderprastha University, Delhi, India
     

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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.

Keywords

Frame, Banach Frame, g−Banach Frame.
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  • On Perturbation of Weighted G−Banach Frames in Banach Spaces

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Authors

Ghanshyam Singh Rathore
Department of Mathematics and Statistics, University College of Science, M.L.S. University, Udaipur, India
Tripti Mittal
Department of Mathematics, Dr. Akhilesh Das Gupta, Institute of Technology and Management, G.G.S. Inderprastha University, Delhi, India

Abstract


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.

Keywords


Frame, Banach Frame, g−Banach Frame.

References





DOI: https://doi.org/10.18311/jims%2F2020%2F21297