FIXED POINTS OF HOLOMORPHIC TRANSFORMATIONS OF OPERATOR BALLS
Mikhail I. Ostrovskii, Victor S. Shulman, Lyudmila Turowska · The Quarterly Journal of Mathematics · 2009
A new technique for proving fixed-point theorems for families of holomorphic transformations of operator balls is developed. One of these theorems is used to show that a bounded group representation in a real or complex Hilbert space is orthogonalizable or unitarizable (that is similar to an orthogonal or unitary representation), respectively, provided the representation has an invariant indefinite quadratic form with finitely many negative squares.