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

الملخص EN

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.