Address:
S.K. Kaushik, Department of Mathematics, Kirori Mal College, University of Delhi, Delhi 110 007, India
Shalu Sharma, Department of Mathematics, University of Delhi, Delhi 110 007, India
E-mail:
shikk2003@yahoo.co.in
shalusharma_21@yahoo.co.in
Abstract: 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.
AMSclassification: primary 42C15; secondary 42C30.
Keywords: frame, Schauder frames.
DOI: 10.5817/AM2014-1-39