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Title: Generalized Schauder frames (English)
Author: Kaushik, S.K.
Author: Sharma, Shalu
Language: English
Journal: Archivum Mathematicum
ISSN: 0044-8753 (print)
ISSN: 1212-5059 (online)
Volume: 50
Issue: 1
Year: 2014
Pages: 39-49
Summary lang: English
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Category: math
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Summary: 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. (English)
Keyword: frame
Keyword: Schauder frames
MSC: 42C15
MSC: 42C30
MSC: 94C15
idZBL: Zbl 06391564
idMR: MR3194767
DOI: 10.5817/AM2014-1-39
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Date available: 2014-04-04T07:18:34Z
Last updated: 2015-03-19
Stable URL: http://hdl.handle.net/10338.dmlcz/143718
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Reference: [12] Liu, R., Zheng, B.: A characterization of Schauder frames which are near Schauder bases.J. Fourier Anal. Appl. 16 (2010), 791–803. Zbl 1210.46012, MR 2673710, 10.1007/s00041-010-9126-5
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