In this paper, we first introduce the notion of controlled weaving K-g-frames in Hilbert spaces. Then, we present sufficient conditions for controlled weaving K-g-frames in separable Hilbert spaces. Also, a characterization of controlled weaving K-g-frames is given in terms of an operator. Finally, we show that if bounds of frames associated with atomic spaces are positively confined, then controlled K-g-woven frames gives ordinary weaving K-frames and vice-versa.

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In this paper, we introduce some new [Formula: see text]-frames related to the adjoint of a [Formula: see text]-frame and sum of two [Formula: see text]-frames in Hilbert spaces. We prove that adjoint of a normal [Formula: see text]-frame is also a [Formula: see text]-frame.