 

Akhlaq A. Siddiqui
Convex combinations of unitaries in JB*algebras view print


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


Abstract
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 24555, Riyadh11451, Kingdom of Saudi Arabia.
asiddiqui@ksu.edu.sa

