New York Journal of Mathematics
Volume 17 (2011) 139-147


Akhlaq A. Siddiqui

The λu-function in JB*-algebras

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


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 λu-function. Our goal here is to extend the notion of a λu-function to the context of JB*-algebras. We study convex combinations of elements in a JB*-algebra using the λu-function and earlier results we have obtained on the geometry of JB*-algebras. A formula to compute λu-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, Riyadh-11451, Kingdom of Saudi Arabia.