Two applications of the subnormality of the Hessenberg matrix related to general orthogonal polynomials (Q549291)

If the support of a measure is real and bounded, then the associated infinite Jacobi matrix \(J\) defines a bounded operator in \(\ell^2\). This operator is also algebraic in the sense that \(J\) is a zero of the equation \(z - \bar{z} = 0\) defining the support. The authors extend this property to the case of measures with bounded support on curves given by polynomials in \(z\) and \(\bar{z}\). In this case the role of \(J\) is played by a certain matrix \(D\). Indeed, the authors establish a noncommutative Cayley-Hamilton type theorem for the matrix \(D\). They also prove a theorem generalizing the Krein theorem for measures not necessarily on the real line.