MultiFrame Vectors for Unitary Systems in Hilbert $C^{*}$modules

In this paper, we focus on the structured multiframe vectors in Hilbert $C^*$modules. More precisely, it will be shown that the set of all complete multiframe 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 multiRiesz vectors, when the surjective operator is replaced by unitary and invertible operators, respectively. Moreover, we show that new multiframes (resp. multiRiesz bases) can be obtained as linear combinations of known ones using coefficients which are operators in a certain class.