LAUSR

In this paper we mainly discuss the exact K-g-frames in the Hilbert spaces. We use the induced sequence $$\{u_{jk}\}$${ujk} of a g-Bessel sequence $$\{\Lambda _j\}_{j\in J}$${Λj}j∈J and an invertible operator to characterize whether $$\{\Lambda _j\}_{j\in J}$${Λj}j∈J is an exact K-g-frame or not, we also use the bounded linear operator K and $$l^2(\{{{\mathcal V}_j}\}_{j\in J})$$l2({Vj}j∈J)-linear independent to characterize the properties of the K-dual sequence of $$\{\Lambda _j\}_{j\in J}$${Λj}j∈J.