Some applications of Berezin θ-sequences and Berezin symbols

We consider the so-called Berezin ?-sequence, where ? is an operator valued inner function, for operators on the vector valued Hardy space H2E (D), and study the invertibility of some operators on the model space K? = H2E ? ?H2E via Berezin ?-sequence. By applying of Berezin symbols technique the Toeplitz corona problem in the Bergman space L2a(D) is studied. Moreover, C-invertibility and C-unitarity of operators are also defined and studied.