Abstract. Controlled frames for spherical wavelets were introduced by Bogdanova et al. to get a numerically more efficient approximation algorithm. In this paper we propose some useful results about controlled K-g-frames, which are generalizations of K-g-frames. We show that if fΛigi2I is a CC0-controlled K-g-frame and U; K are bounded linear operators in a separable Hilbert space, then, under certain conditions, the sequences of operatorsfΛiUgi2I, fΛiU ∗gi2I are also CC0-controlled K-gframes. We also present the concept of CC0-controlled K-g-dual frame and extend some known equalities and inequalities. Finally we study the stability problem for perturbation of CC0-controlled K-g-frames.
