G-frames as special frames

Authors: ABAS ASKARIZADEH, MOHAMMAD ALI DEHGHAN

Abstract: G-frames are generalizations of ordinary frames for Hilbert spaces. In the present paper we study frames, and operators on a special separable Hilbert C^*-module, B(H,K), where H and K are Hilbert spaces, and we prove that every g-frame for H is a frame for B(H,K) and vice versa. Also, we derive some relationships between g-Riesz bases for H and Riesz bases in B(H,K). Similar results for orthogonal bases will be discussed.

Keywords: Hilbert C^*-module, Frame, g-Frame, Riesz basis, g-Riesz basis, Orthogonal basis, g-Orthonormal basis

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