Redundancy of g-frames

Abstract

Already, a quantitative notion of redundancy for finite frames was introduced by Bodmann et al. (Appl Comput Harmon Anal 30:348–362, 2011). In this paper, we introduce the notion of redundancy for g-frames. We define redundancy function of a g-frame on the unit sphere of a Hilbert space H. Then by considering the infimum and supremum values of redundancy function, which are called lower and upper redundancies, we study the concept of redundancy for g-frames. Also, we define this notion in case of infinite g-frames and verify its characteristics. Finally, we provide some examples in both finite and infinite cases.