Abstract
We consider the so-called Berezin theta- sequence, where theta is an operator valued inner function, for operators on the vector valued Hardy space H-E(2) (ID) , and study the invertibility of some operators on the model space K-theta = H-E(2) circle minus theta H-E(2) via Berezin theta- sequence. By applying of Berezin symbols technique the Toeplitz corona problem in the Bergman space L-a(2) (ID) is studied. Moreover, C- invertibility and C-unitarity of operators are also defined and studied.