Geodesic
Generalized Schauder frames
Archivum mathematicum, Tome 50 (2014) no. 1, pp. 39-49 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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Schauder frames were introduced by Han and Larson [9] and further studied by Casazza, Dilworth, Odell, Schlumprecht and Zsak [2]. In this paper, we have introduced approximative Schauder frames as a generalization of Schauder frames and a characterization for approximative Schauder frames in Banach spaces in terms of sequence of non-zero endomorphism of finite rank has been given. Further, weak* and weak approximative Schauder frames in Banach spaces have been defined. Finally, it has been proved that $E$ has a weak approximative Schauder frame if and only if $E^*$ has a weak* approximative Schauder frame.
Schauder frames were introduced by Han and Larson [9] and further studied by Casazza, Dilworth, Odell, Schlumprecht and Zsak [2]. In this paper, we have introduced approximative Schauder frames as a generalization of Schauder frames and a characterization for approximative Schauder frames in Banach spaces in terms of sequence of non-zero endomorphism of finite rank has been given. Further, weak* and weak approximative Schauder frames in Banach spaces have been defined. Finally, it has been proved that $E$ has a weak approximative Schauder frame if and only if $E^*$ has a weak* approximative Schauder frame.
DOI : 10.5817/AM2014-1-39
Classification : 42C15, 42C30, 94C15
Keywords: frame; Schauder frames 
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Kaushik, S.K.; Sharma, Shalu. Generalized Schauder frames. Archivum mathematicum, Tome 50 (2014) no. 1, pp. 39-49. doi: 10.5817/AM2014-1-39

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