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The Quarterly Journal of Mathematics Advance Access published online on October 21, 2009
The Quarterly Journal of Mathematics, doi:10.1093/qmath/hap031
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© 2009. Published by Oxford University Press. All rights reserved. For permissions, please email: journals.permissions@oxfordjournals.org

FIXED POINTS OF HOLOMORPHIC TRANSFORMATIONS OF OPERATOR BALLS

M. I. Ostrovskii{dagger}

Department of Mathematics and Computer Science, St. John's University, 8000 Utopia Parkway, Queens, NY 11439, USA

S. Shulman {ddagger}

Department of Mathematics, Vologda State Technical University, 15 Lenina street, Vologda 160000, Russia

L. Turowska §

Department of Mathematical Sciences, Chalmers University of Technology and University of Gothenburg, Gothenburg SE-41296, Sweden

{dagger} Corresponding author. E-mail: ostrovsm{at}stjohns.edu

Received 24 March 2009; revised 30 August 2009
  Abstract

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.

{ddagger} E-mail: shulman_v{at}yahoo.com

§ E-mail: turowska{at}chalmers.se


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