C-FRAMES AND C-BESSEL MAPPINGS

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.