%0 Journal Article
%T c-Frames and c-Bessel mappings
%J Bulletin of the Iranian Mathematical Society
%I Iranian Mathematical Society (IMS)
%Z 1017-060X
%A Faroughi, M.
%A Osgooei, E.
%D 2012
%\ 04/01/2012
%V 38
%N 1
%P 203-222
%! c-Frames and c-Bessel mappings
%K Lebesque integral
%K Hilbert space
%K C*-algebra
%K trace class operator
%K frame theory
%R
%X 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.
%U http://bims.iranjournals.ir/article_401_8c30c121871d0918061a85cbc216a1ae.pdf