Means of unitaries, conjugations, and the Friedrichs operator ✩

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. © 2007 Elsevier Inc. All rights reserved