New York Journal of Mathematics
Volume 19 (2013) 145-158


Akhlaq A. Siddiqui

Computation of the λu-function in JB*-algebras

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

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 λu-function, the present author recently initiated a study of the λu-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 λu-function on invertible elements in a JB*-algebra. The main purpose in this article is to investigate the computation of the λu-function on noninvertible elements in the unit ball of a JB*-algebra. Additional results that relate the λu-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 2455-5, Riyadh-11451, Kingdom of Saudi Arabia.