Exact Continuous frames in Hilbert C*-modules

TL;DR

This paper explores the properties of duals of continuous frames in Hilbert C*-modules, focusing on conditions under which removing elements affects the frame structure.

Contribution

It provides new criteria for the stability of continuous frames in Hilbert C*-modules when elements are removed.

Findings

Identifies conditions for a set to remain a continuous frame after element removal

Characterizes duals of continuous frames in Hilbert C*-modules

Establishes criteria for the non-removability of elements in continuous frames

Abstract

In the present paper, we investigate some properties of duals of continuous frames in Hilbert C*-modules. In particular, we give requirements so that by removing some elements of a continuous frame, it does not remain a continuous frame and when the remaining set still remains a continuous frame.