 

Akhlaq A. Siddiqui
The λ_{u}function in JB*algebras view print


Published: 
February 27, 2011 
Keywords: 
C*algebra; JB*algebra; unit ball; invertible element; spectrum; unitary element; unitary isotope; convex hull; λ_{u}function 
Subject: 
17C65, 46L05, 46H70 


Abstract
Inspired by work of R. M. Aron and R. H. Lohman, Gert K. Pedersen introduced a
geometric function, which is defined on the unit ball of a C*algebra and
called the λ_{u}function. Our goal here is to extend the notion of a
λ_{u}function to the context of JB*algebras. We study convex
combinations of elements in a JB*algebra using the λ_{u}function
and earlier results we have obtained on the geometry of JB*algebras. A
formula
to compute λ_{u}function is obtained for invertible
elements in a JB*algebra. In the course of our analysis, some
C*algebra results due to G. K. Pedersen,
C. L. Olsen and M. R\o rdam are extended to general
JB*algebras.


Author information
Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh11451, Kingdom of Saudi Arabia.
asiddiqui@ksu.edu.sa

