The concept of -frame which is a generalization of the frame in Hilbert spaces generated by the bilinear mapping is considered. -frame operator is defined; analogues of some well-known results of frame theory are obtained in Hilbert spaces. Conditions for the existence of -frame in Hilbert spaces are obtained; the relationship between the definite bounded surjective operator and -frame is also studied. The concept of -orthonormal -basis is introduced.
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