@article { author = {Abdollahpour, M.}, title = {Dilation of a family of g-frames}, journal = {Wavelet and Linear Algebra}, volume = {1}, number = {1}, pages = {9-18}, year = {2014}, publisher = {Vali-e-Asr university of Rafsanjan}, issn = {2383-1936}, eissn = {2476-3926}, doi = {}, abstract = {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.}, keywords = {g-Riesz basis,G-Frame,disjointnes}, url = {https://wala.vru.ac.ir/article_6347.html}, eprint = {https://wala.vru.ac.ir/article_6347_0ea5a42f7e87f2c43f8086abf7878646.pdf} }