# On unitary convex decompositions of vectors in a $JB^{*}$-algebra

## Akhlaq A. Siddiqui

Address: Department of Mathematics, College of Science, King Saud University P.O.Box 2455-5, Riyadh-11451, Kingdom of Saudi Arabia

E-mail: asiddiqui@ksu.edu.sa

Abstract: By exploiting his recent results, the author further investigates the extent to which variation in the coefficients of a unitary convex decomposition of a vector in a unital $JB^{*}$-algebra permits the vector decomposable as convex combination of fewer unitaries; certain $ C^{*}$-algebra results due to M. RĂ¸rdam have been extended to the general setting of $JB^{*}$-algebras.

AMSclassification: primary 17C65; secondary 46L70, 46H70.

Keywords: C^{*}-algebra, JB^{*}-algebra, unit ball, invertible element, unitary element, unitary isotope, convex hull, unitary rank, unitary convex decomposition.

DOI: 10.5817/AM2013-2-79