We mainly discuss K-g-frames and its duality. First, we explore the relationship between K-g-frames and g-frames. Then, we give some sufficient conditions under which the sum of K-g-frames and g-Bessel sequences with bounded linear operator or nonzero complex bounded sequence is still K-g-frames. In addition, we also give two special forms about the sum of K-g-frames. Finally, we research the duality of K-g-frames in closed subspace R(K), and the ways of constructing the K-g-frames by using the approximate duality.
Chun Nian DAI, Jin Song LENG, Miao HE. K-g-frames and Their Duality. Acta Mathematica Sinica, Chinese Series, 2021, 64(2): 243-254 https://doi.org/10.12386/A2021sxxb0021
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