University of MaraghehSahand Communications in Mathematical Analysis2322-580715120190701Multi-Frame Vectors for Unitary Systems in Hilbert $C^{*}$-modules1183496810.22130/scma.2018.77908.356ENMohammadMahmoudiehSchool of Mathematics and computer Science, Damghan University, Damghan, Iran.HessamHosseinnezhadSchool of Mathematics and computer Science, Damghan University, Damghan, Iran.GholamrezaAbbaspour TabadkanSchool of Mathematics and computer Science, Damghan University, Damghan, Iran.Journal Article20171223In 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.https://scma.maragheh.ac.ir/article_34968_32b4b532a24202b9716e9e3469083a0a.pdf