c-Frames and c-Bessel mappings

Document Type : Research Paper


1 Islamic Azad University

2 University of Tabriz


The theory of c-frames and c-Bessel mappings are the generalizations
of the theory of frames and Bessel sequences. In this paper, we
obtain several equivalent conditions for dual of c-Bessel mappings.
We show that for a c-Bessel mapping $f$, a retrieval
formula with respect to a c-Bessel mapping $g$ is satisfied if and
only if $g$ is sum of the canonical dual of $f$ with a c-Bessel
mapping which  weakly belongs to the null space of the pre-frame operator
of $f$. Also, we prove that composition of pre-frame operator with
analysis operator of two square norm integrable c-Bessel mappings
are trace class operators.