Characterization of duals of continuous frames in Hilbert C*-modules

Abstract

In this paper, we investigate some characterizations of dual continuous frames and give some results about them. Also, we refer to the method of constructing a family of duals through a fixed dual and show there exists a one-to-one correspondence between duals of a continuous frame for Hilbert $C^{\ast }$-module $U$ and adjointable operators $K$ from $U$ to $L^2(\Omega ,\mathcal{A})$. Then we check the conditions that the sum of two duals of a given continuous frame under the influence of adjointable mappings becomes a dual of it and state some results about them.

arXiv admin note: text overlap with arXiv:2208.14012, arXiv:2208.06799