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

summary: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. Rørdam have been extended to the general setting of $JB^{*}$-algebras