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.