@article { author = {Mahmoudieh, Mohammad and Hosseinnezhad, Hessam and Abbaspour Tabadkan, Gholamreza}, title = {Multi-Frame Vectors for Unitary Systems in Hilbert $C^{*}$-modules}, journal = {Sahand Communications in Mathematical Analysis}, volume = {15}, number = {1}, pages = {1-18}, year = {2019}, publisher = {University of Maragheh}, issn = {2322-5807}, eissn = {2423-3900}, doi = {10.22130/scma.2018.77908.356}, abstract = {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.}, keywords = {Multi-frame vector,Wandering vector,Local commutant,Unitary system}, url = {https://scma.maragheh.ac.ir/article_34968.html}, eprint = {https://scma.maragheh.ac.ir/article_34968_32b4b532a24202b9716e9e3469083a0a.pdf} }