On redundancy, dilations and canonical duals of $g$-frames in Hilbert spaces

Abstract

In Hilbert spaces, the redundancy property of $g$-frames is different from that of frames, and the dilation theory is interesting and important in many mathematical fields. In this paper, we study the redundancy and dilations of $g$-frames in Hilbert spaces. First, we characterize $g$-Riesz bases and exact $g$-frames under some constraints, then obtain some dilation results for (normalized tight) $g$-frames, and give some properties about them. Finally we prove some interesting properties on the canonical duals of $g$-frames.