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Generalized atomic subspaces for operators in Hilbert spaces

Prasenjit Ghosh, Tapas Kumar Samanta (2022)

Mathematica Bohemica

We introduce the notion of a g -atomic subspace for a bounded linear operator and construct several useful resolutions of the identity operator on a Hilbert space using the theory of g -fusion frames. Also, we shall describe the concept of frame operator for a pair of g -fusion Bessel sequences and some of their properties.

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...

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