G-frames as special frames

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.