 

Mubariz Garayev
On the invertibility of operators on a model space
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Published: 
March 15, 2024. 
Keywords: 
Interpolation Blaschke product, reproducing kernel, Berezin symbol, invertibility of operators. 
Subject [2010]: 
47A35, 47B20. 


Abstract
For a scalar inner function θ, the model space of Sz.Nagy and Foias
is the subspace K_{θ} = H^{2} ⊖ θ H^{2}
of the classical Hardy space H^{2} 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.


Acknowledgements
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.


Author information
Mubariz Garayev
Department of Mathematics
College of Science
King Saud University
Riyadh, Saudi Arabia
mgarayev@ksu.edu.sa

