Canonical Dual $K$-g-Bessel Sequences and $K$-g-Frame Sequences

The classical canonical dual for a K-g-frame is absent since the frame operator may not be invertible. We introduce the concept of canonical dual K-g-Bessel sequences, which have some properties similar to classical canonical dual, to investigate the duality of K-g-frames. We obtain the exact form of the canonical dual K-g-Bessel sequences for Parseval K-g-frames and some other related results. We also introduce the concept of K-g-frame sequences to explore the properties of local K-g-frames. We present a necessary and sufficient condition under which a K-g-frame sequence is a K-g-frame, and necessary and sufficient conditions for a sequence of bounded operators to be a K-g-frame sequence. We end the paper by examining the relationship between K-g-frame sequences and g-frames for closed subspaces, and the relationship between two K-g-frame sequences and the ranges of the involved operators.