c-Frames and c-Bessel mappings


Research Paper

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