 

Akhlaq A. Siddiqui
Computation of the λ_{u}function in JB*algebras view print


Published: 
May 22, 2013 
Keywords: 
C*algebra; JB*algebra; unit ball; invertible element; unitary element; unitary isotope; convex hull; λ_{u}function 
Subject: 
17C65, 46L05, 46H70 


Abstract
Motivated by the work of Gert K. Pedersen on a geometric function, which is defined on the unit ball of a C*algebra and
called the λ_{u}function, the present author recently initiated a study of the λ_{u}function in the more general setting of JB*algebras. He used his earlier results on the geometry of the unit ball to investigate certain convex combinations of elements in a JB*algebra and to obtain analogues of some related C*algebra results, including a formula to compute λ_{u}function on invertible elements in a JB*algebra. The main purpose in this article is to investigate the computation of the λ_{u}function on noninvertible elements in the unit ball of a JB*algebra. Additional results that relate the λ_{u}function to convex combinations, unitary rank, and distance to the invertibles in the C*algebra setting are generalized to the JB*algebra context. Results of G. K. Pedersen and M. Rordam are generalized. An open problem is presented.


Author information
Department of Mathematics, College of Science, King Saud University, P.O. Box 24555, Riyadh11451, Kingdom of Saudi Arabia.
asiddiqui@ksu.edu.sa

