{"title":"On Perturbation of Weighted G−Banach Frames in Banach Spaces","authors":"G. S. Rathore, Tripti Mittal","doi":"10.18311/JIMS/2020/21297","DOIUrl":null,"url":null,"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.","PeriodicalId":38246,"journal":{"name":"Journal of the Indian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2020-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of the Indian Mathematical Society","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.18311/JIMS/2020/21297","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"Mathematics","Score":null,"Total":0}
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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.
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The Society began publishing Progress Reports right from 1907 and then the Journal from 1908 (The 1908 and 1909 issues of the Journal are entitled "The Journal of the Indian Mathematical Club"). From 1910 onwards,it is published as its current title ''the Journal of Indian Mathematical Society. The four issues of the Journal constitute a single volume and it is published in two parts: issues 1 and 2 (January to June) as one part and issues 3 and 4 (July to December) as the second part. The four issues of the Mathematics Student (another periodical of the Society) are published as a single yearly volume. Only the original research papers of high quality are published in the Journal of Indian Mathematical Society.
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