A note on tetrablock contractions (Q903730)

Commuting triples \((A,B,P)\) of bounded linear operators on a Hilbert space \(\mathcal H\) that are tetrablock contractions in the sense of \textit{T. Bhattacharyya} [Indiana Univ. Math. J. 63, No. 6, 1601--1629 (2014; Zbl 1312.47014)] are studied in this paper. A Beurling-Lax-Halmos type theorem and Sz.Nagy-Foias-type functional model for tetrablock contractions are the main results of the author. Moreover, a necessary and sufficient condition is given under which two tetrablock contractions \((A,B,P)\) and \((A',B',P')\) are unitarily equivalent.