Multi-Frame Vectors For Unitary Systems in Hilbert C^∗- Modules

In this paper, we focus on the structured multi-frame vectors in hilbert c^∗-modules. more precisely, it will be shown that the set of all complete multi-frame vectors for a unitary system can be parameterized by the set of all surjective operators, in the local commutant. similar results hold for the set of all complete wandering vectors and complete multi-riesz vectors, when the surjective operator is replaced by unitary and invertible operators, respectively. moreover, we show that new multi-frames (resp. multi-riesz bases) can be obtained as linear combinations of known ones using coefficients which are operators in a certain class.