Dilation of a family of g frames

In this paper, we first discuss about canonical dual of g frameΛP = {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 orthogonalprojection from H onto a closed subspace M. Next, we provethat, 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 Hand K, and Λ and Θ are unitarily equivalent (similar), then Λand Θ can not be weakly disjoint. On the other hand, we studydilation property for g frames and we show that two g framesfor a Hilbert space have dilation property, if they are disjoint,or they are similar, or one of them is similar to a dual g frameof another one. We also prove that a family of g frames for aHilbert space has dilation property, if all the members in thatfamily have the same deficiency.