TY - JOUR
ID - 34968
TI - Multi-Frame Vectors for Unitary Systems in Hilbert $C^{*}$-modules
JO - Sahand Communications in Mathematical Analysis
JA - SCMA
LA - en
SN - 2322-5807
AU - Mahmoudieh, Mohammad
AU - Hosseinnezhad, Hessam
AU - Abbaspour Tabadkan, Gholamreza
AD - School of Mathematics and computer Science, Damghan University, Damghan, Iran.
Y1 - 2019
PY - 2019
VL - 15
IS - 1
SP - 1
EP - 18
KW - Multi-frame vector
KW - Wandering vector
KW - Local commutant
KW - Unitary system
DO - 10.22130/scma.2018.77908.356
N2 - 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.
UR - http://scma.maragheh.ac.ir/article_34968.html
L1 - http://scma.maragheh.ac.ir/article_34968_32b4b532a24202b9716e9e3469083a0a.pdf
ER -