Weaving continuous generalized frames for operators

Recently, Bemrose et al. \cite{BE} developed a theory of weaving frames, which was motivated by a problem regarding distributed signal processing. In this present article, we introduce the atomic $g$-system and we generalize some of the known results in continuous $L$-frames, weaving continuous and weaving continuous $g$-frames, also we study weaving continuous $L$-$g$-frames in Hilbert spaces. Moreover, we study the behaviour continuous $L$-$g$-frames under some perturbations, and we show that approximate $L$-duals are stable under small perturbation and that it is possible to remove some elements of a woven continuous $L$-$g$-frame and still have a woven continuous $L$-$g$-frame.