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Means of unitaries, conjugations, and the Friedrichs operator
Authors:Stephan Ramon Garcia
Institution:Department of Mathematics, Pomona College, Claremont, CA 91711, USA
Abstract:If C is a conjugation (an isometric, conjugate-linear involution) on a separable complex Hilbert space H, then TB(H) is called C-symmetric if T=CTC. In this note we prove that each C-symmetric contraction T is the mean of two C-symmetric unitary operators. We discuss several corollaries and an application to the Friedrichs operator of a planar domain.
Keywords:Complex symmetric operator  Complex symmetric matrix  Conjugation  Extreme point  Unilateral shift  Unitary operator  Hankel matrix  Toeplitz matrix  Bergman space  Bergman kernel  Friedrichs operator  Quadrature domain
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