%0 Journal Article
%T Dilation of a family of g-frames
%J Wavelet and Linear Algebra
%I Vali-e-Asr university of Rafsanjan
%Z 2383-1936
%A Abdollahpour, M.
%D 2014
%\ 08/01/2014
%V 1
%N 1
%P 9-18
%! Dilation of a family of g-frames
%K g-Riesz basis
%K G-Frame
%K disjointnes
%R
%X 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.
%U https://wala.vru.ac.ir/article_6347_0ea5a42f7e87f2c43f8086abf7878646.pdf