On a Generalization of the Hilbert Frame Generated by the Bilinear Mapping

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