c-Frames and c-Bessel mappings

Abstract

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