$K$-g-frames and stability of $K$-g-frames in Hilbert spaces
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A $K$-g-frame is a generalization of a g-frame. It can be used to reconstruct elements from the range of a bounded linear operator $K$ in Hilbert spaces. $K$-g-frames have a certain advantage compared with g-frames in practical applications. In this paper, the interchangeability of two g-Bessel sequences with respect to a $K$-g-frame, which is different from a g-frame, is discussed. Several construction methods of $K$-g-frames are also proposed. Finally, by means of the methods and techniques in frame theory, several results of the stability of $K$-g-frames are obtained.
Abstract
A $K$-g-frame is a generalization of a g-frame. It can be used to reconstruct elements from the range of a bounded linear operator $K$ in Hilbert spaces. $K$-g-frames have a certain advantage compared with g-frames in practical applications. In this paper, the interchangeability of two g-Bessel sequences with respect to a $K$-g-frame, which is different from a g-frame, is discussed. Several construction methods of $K$-g-frames are also proposed. Finally, by means of the methods and techniques in frame theory, several results of the stability of $K$-g-frames are obtained.
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