On Sum and Stability of Continuous G-Frames

In this paper, we give some conditions under which the finite sum of continuous g-frames is again a continuous g-frame. We give necessary and sufficient conditions for the continuous g-frames Λ = {Λw ∈ B (H, Kw) : w ∈ Ω} and Γ = {Γw ∈ B (H, Kw) : w ∈ Ω} and operators U and V on H such that ΛU +ΓV = {ΛwU +ΓwV ∈ B (H, Kw) : w ∈ Ω} is again a continuous g-frame. Moreover, we obtain some sufficient conditions under which the finite sum of con tinuous g-frames are stable under small perturbations.