Some relations between continuous generalized frames

Abstract

Generalized frames are natural generalizations of frames. The computation of distances between frames is a crucial concept in frame theory. In this paper we give some basic definitions and results on continuous frames, continuous g-frames, equivalence relations and distances between continuous g-frames. Furthermore, we introduce some equivalency relations between continuous g-frames for a Hilbert space and closed subspaces of \(L^{2}({\mathfrak {A}})\), and we define a distance between continuous g-frames. Finally, we define a new metric on the set of near continuous g-frames and investigate some of its properties.