Minimizing transformations of Hermitian functionals, and product integration

In this contribution we are focused on some spectral transformations of Hermitian linear functionals. They are the analogues of the Christoffel transform for linear functionals, i. e. for Jacobi matrices which has been deeply studied in the past. We consider Hermitian linear functionals associated with a probability measure supported on the unit circle. In such a case we compare the Hessenberg matrices associated with such a probability measure and its Christoffel transform. In this way, almost unitary matrices appear. We obtain the deviation to the unit matrix both for principal submatrices and the complete matrices respectively.

Semiorthogonal functions and orthogonal polynomials on the unit circle

Hermitian Functionals on B-Algebras and Duality Characterizations of C ∗ -Algebras

Some remarks on almost Hermitian functionals