TY - JOUR
ID - 6347
TI - Dilation of a family of g-frames
JO - Wavelet and Linear Algebra
JA - WALA
LA - en
SN - 2383-1936
AU - Abdollahpour, M.
AD - Department of Mathematics, Faculty of Mathematical Sciences, University of Mohaghegh
Ardabili, Ardabil, Islamic Republic of Iran
Y1 - 2014
PY - 2014
VL - 1
IS - 1
SP - 9
EP - 18
KW - g-Riesz basis
KW - G-Frame
KW - disjointnes
DO -
N2 - In this paper, we first discuss about canonical dual of g-frame ΛP = {ΛiP ∈ B(H, Hi) : i ∈ I}, where Λ = {Λi ∈ B(H, Hi) : i ∈ I} is a g-frame for a Hilbert space H and P is the orthogonal projection from H onto a closed subspace M. Next, we prove that, if Λ = {Λi ∈ B(H, Hi) : i ∈ I} and Θ = {Θi ∈ B(K, Hi) : i ∈ I} be respective g-frames for non zero Hilbert spaces H and K, and Λ and Θ are unitarily equivalent (similar), then Λ and Θ can not be weakly disjoint. On the other hand, we study dilation property for g-frames and we show that two g-frames for a Hilbert space have dilation property, if they are disjoint, or they are similar, or one of them is similar to a dual g-frame of another one. We also prove that a family of g-frames for a Hilbert space has dilation property, if all the members in that family have the same deficiency.
UR - https://wala.vru.ac.ir/article_6347.html
L1 - https://wala.vru.ac.ir/article_6347_0ea5a42f7e87f2c43f8086abf7878646.pdf
ER -