Means of Unitaries, Conjugations, and the Friedrichs Operator

Authors

Stephan Ramon Garcia, Pomona CollegeFollow

Document Type

Article

Department

Mathematics (Pomona)

Publication Date

2007

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

Abstract

If C is a conjugation (an isometric, conjugate-linear involution) on a separable complex Hilbert space H, thenT∈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.

Rights Information

© 2007 Elsevier B.V.

Terms of Use & License Information

Terms of Use for work posted in Scholarship@Claremont.

DOI

10.1016/j.jmaa.2007.01.094

Recommended Citation

Stephan Ramon Garcia, Means of unitaries, conjugations, and the Friedrichs operator, Journal of Mathematical Analysis and Applications, Volume 335, Issue 2, 15 November 2007, Pages 941-947, ISSN 0022-247X, http://dx.doi.org/10.1016/j.jmaa.2007.01.094. (http://www.sciencedirect.com/science/article/pii/S0022247X07001424)