New York Journal of Mathematics
Volume 17 (2011) 127-137


Akhlaq A. Siddiqui

Convex combinations of unitaries in JB*-algebras

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Published: February 27, 2011
Keywords: C*-algebra; JB*-algebra; invertible element; positive elements; unitary element; unitary isotope
Subject: 17C65, 46K70, 46L05, 46L45, 46L70

We continue our recent efforts to exploit the notion of a unitary isotope to study convex combinations of unitaries in an arbitrary JB*-algebra. Exact analogues of C*-algebraic results, due to R. V. Kadison, C. L. Olsen and G. K. Pedersen, are proved for general JB*-algebras. We show that if a contraction in a JB*-algebra is a convex combination of n unitaries, then it is also a mean of n unitaries. This generalizes a well known theorem of Kadison and Pedersen. Our methods also provide alternative proofs of other results for C*-algebras.

Author information

Department of Mathematics, College of Science, King Saud University, P.O. Box 2455-5, Riyadh-11451, Kingdom of Saudi Arabia.