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.
Hilbert C^*-module, Frame, g-Frame, Riesz basis, g-Riesz basis, Orthogonal basis, g-Orthonormal basis
ASKARIZADEH, ABAS and DEHGHAN, MOHAMMAD ALI
"G-frames as special frames,"
Turkish Journal of Mathematics: Vol. 37:
1, Article 7.
Available at: https://journals.tubitak.gov.tr/math/vol37/iss1/7