Constructions of \(K\text{-g}\)-frames and tight \(K\text{-g}\)-frames in Hilbert spaces (Q2210201)

The authors construct \(K\text{-g}\)-frames from a \(K\)-frame and a g-Bessel sequence. They also find a new constrictive way of generating a \(K\text{-g}\)-frame from two existing \(K\text{-g}\)-frames by using a relation between a positive operator and the frame operator of a \(K\text{-g}\)-frame. A necessary and sufficient condition for the existence of a tight \(K\text{-g}\)-frame from a pair of two g-frames is provided. The authors also provide some examples.