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Means of unitaries, conjugations, and the Friedrichs operator |
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| Authors: | Stephan Ramon Garcia |
| Affiliation: | 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 T∈B(H) is called C-symmetric if T=CT∗C. 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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