For a scalar inner function θ, the model space of Sz.-Nagy and Foias is the subspace K_θ = H² ⊖ θ H² of the classical Hardy space H² over the unit disc D in the complex plane C. We shall consider the following question: if A is a bounded linear operator on the model space K_θ such that the Berezin symbol function of A is bounded below, under which additional conditions is A invertible? In this article we investigate this question in the case when θ is an interpolation Blaschke product. In particular, the invertibility property of functions of model operators is investigated. Some other problems are also discussed.

The author would like to extends his appreciation to the Distinguished Scientist Fellowship Program at King Saud University, Riyadh, Saudi Arabia, for funding this work through Researchers Supporting Project number RSPD2024R1056.