We employ a new reverse Carleson type condition and define sampling to study closed range composition operators on BMOA. provide necessary also sufficient conditions for operator be show that is as an from the Bloch space BMOA if only it bounded below all Möbius transformations.

in this paper, we state some results on product of operators with closed rangesand we solve the operator equation txs*- sx*t*= a in the general setting of theadjointable operators between hilbert c*-modules, when ts = 1. furthermore, by usingsome block operator matrix techniques, we nd explicit solution of the operator equationtxs*- sx*t*= a.