TY - JOUR ID - 401 TI - c-Frames and c-Bessel mappings JO - Bulletin of the Iranian Mathematical Society JA - BIMS LA - en SN - 1017-060X AU - Faroughi, M. AU - Osgooei, E. AD - Islamic Azad University AD - University of Tabriz Y1 - 2012 PY - 2012 VL - 38 IS - 1 SP - 203 EP - 222 KW - Lebesque integral KW - Hilbert space KW - C*-algebra KW - trace class operator KW - frame theory DO - N2 - 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. UR - http://bims.iranjournals.ir/article_401.html L1 - http://bims.iranjournals.ir/article_401_8c30c121871d0918061a85cbc216a1ae.pdf ER -