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Generalized Schauder frames

S.K. Kaushik;  Shalu Sharma — 2014

Archivum Mathematicum

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...

On the existence of non-linear frames

Shah Jahan;  Varinder Kumar;  S.K. Kaushik — 2017

Archivum Mathematicum

A stronger version of the notion of frame in Banach space called Strong Retro Banach frame (SRBF) is defined and studied. It has been proved that if 𝒳 is a Banach space such that 𝒳 * has a SRBF, then 𝒳 has a Bi-Banach frame with some geometric property. Also, it has been proved that if a Banach space 𝒳 has an approximative Schauder frame, then 𝒳 * has a SRBF. Finally, the existence of a non-linear SRBF in the conjugate of a separable Banach space has been proved.

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