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The Quarterly Journal of Mathematics Advance Access published online on October 30, 2007
The Quarterly Journal of Mathematics, doi:10.1093/qmath/ham042
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© 2007. Published by Oxford University Press. All rights reserved. For permissions, please email: journals.permissions@oxfordjournals.org

ORTHOGONALLY ADDITIVE POLYNOMIALS ON C*-ALGEBRAS

C. Palazuelos {dagger}

Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad Complutense de Madrid, Madrid 28040, Spain

A. M. Peralta{ddagger}

Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Granada, 18071 Granada, Spain

I. Villanueva §

Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad Complutense de Madrid, Madrid 28040, Spain

{ddagger} Corresponding author. E-mail: aperalta{at}ugr.es

Received 2 March 2007; revised 20 June 2007
  Abstract

We show that for every orthogonally additive scalar n-homogeneous polynomial P on a C*-algebra A there exists {varphi} in A* satisfying P(x)={varphi} (xn), for each element x in A. The vector-valued analogue follows as a corollary.

{dagger} E-mail: carlospalazuelos{at}mat.ucm.es

§ E-mail: ignaciov{at}mat.ucm.es


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