Weekly seminar on December 23.12.2015, 10:00 a.m. will feature a report by corresponding member of ANAS, professor, head of the Department of Non-harmonic Analysis Bilal Telman oglu Bilalov, entitled “Some questions of atomic decompositions and frames”.
In report frames in Hilbert and Banach spaces are considered and their properties in the context of Noetherian mapping are studied in this paper. Atomic decompositions in Banach spaces are also considered. The concept of K -closeness is introduced. The stability of frame properties and atomic decompositions with respect to K -closeness is proved. The concept of t-frame associated with the tensor product of Hilbert spaces is introduced. All the properties of ordinary frames are extended to this case. Noetherian perturbation of t-frames is considered. The stability of t -frameness with respect to quadratic closeness is proved.