Disjointness of continuous g-frames and Riesz-type continuous g-frames

TL;DR

This paper explores the properties of disjointness in continuous g-frames within Hilbert spaces, establishing equivalences, constructing new frames, and analyzing Riesz-type frames to deepen understanding of their structure.

Contribution

It introduces disjointness concepts for continuous g-frames, provides equivalent conditions, and constructs new frames, advancing the theoretical framework of g-frames.

Findings

Disjoint, strongly disjoint, and weakly disjoint continuous g-frames are characterized.

Equivalent conditions for disjointness notions are established.

A method to construct continuous g-frames from disjoint frames is presented.

Abstract

In this paper we introduce concepts of disjoint, strongly disjoint and weakly disjoint continuous $g$-frames in Hilbert spaces and we get some equivalent conditions to these notions. We also construct a continuous g-frame by disjoint continuous g-frames. Furthermore, we provide some results related to the Riesz-type continuous $g$-frames.