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- W2890766364 abstract "Gavruta [L. Gavruta, Frames for operators, Appl. Comput. Harmon. Anal. 32 (2012) 139–144] introduced the notion of [Formula: see text]-frame and atomic system for an operator [Formula: see text] in Hilbert spaces. We extend these notions to Banach spaces and obtain various new results. A necessary and sufficient condition for the existence of an atomic system for an operator [Formula: see text] in a Banach space is given. Also, a characterization for the family of local atoms of subspaces of Banach spaces has been given. Further, we give methods to construct an atomic system for an operator [Formula: see text] from a given Bessel sequence and an [Formula: see text]-Bessel sequence. Finally, a result related to stability of atomic system for an operator [Formula: see text] in a Banach space has been given." @default.
- W2890766364 created "2018-09-27" @default.
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- W2890766364 date "2019-01-01" @default.
- W2890766364 modified "2023-10-18" @default.
- W2890766364 title "Atomic systems for operators" @default.
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- W2890766364 doi "https://doi.org/10.1142/s0219691318500662" @default.
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