University of Mostaganem, Route Nationale 11, Mostaganem, 27000, Algeria
E-mail: bbendoukha@gmail.com

Received March 27, 2020, revised July 16, 2020.

Abstract

The present paper is aimed to study a certain class of pairs of operators
having the symmetrized bidisk as a spectral set. For such pairs, the conditions of Г-contractivity are given and the functional model is constructed.
Some criteria of unitary equivalence are also established.

Mathematics Subject Classification 2010: 47A20, 47A25 Key words: functional model, fundamental operator, pure contraction, spectral set, symmetrized bidisc