On a Generalization of the Hilbert Frame Generated by the Bilinear Mapping. (5th April 2016) - Ismailov, Migdad; Guliyeva, Fatima; Nasibov, Yusif
Abstract : The concept of b -frame which is a generalization of the frame in Hilbert spaces generated by the bilinear mapping is considered. b -frame operator is defined; analogues of some well-known results of frame theory are obtained in Hilbert spaces. Conditions for the existence of b -frame in Hilbert spaces are obtained; the relationship between the definite bounded surjective operator and b -frame is also studied. The concept of b -orthonormal b -basis is introduced.