Christoffel transforms and Hermitian linear functionals

8 pages, no figures.-- MSC2000 codes: Primary 42C05; Secondary 15A23.MR#: MR2192525 (2006h:42044)Zbl#: Zbl 1121.42017In 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.The work of the first author (F. Marcellán) was supported by Dirección General de Investigación, Ministerio de Educación y Ciencia of Spain, under grant BFM 2003-06335-C03-02, and INTAS Research Network NeCCA INTAS 03-51-6637. The work of the second author (J. Hernández) was supported by Fundación Universidad Carlos III de Madrid.Publicad