Asymmetric decompositions of vectors in $JB^*$-algebras

Akhlaq A. Siddiqui

Department of Mathematics, The University of Lahore,1Km Raiwind Road, Lahore, Pakistan



By investigating the extent to which variation in the coefficients of a convex combination of unitaries in a unital $JB^{*}$-algebra permits that combination to be expressed as convex combination of fewer unitaries of the same algebra, we generalise various results of R.\ V.\ Kadison and G.\ K.\ Pedersen.

    In the sequel, we shall give a couple of characterisations of $JB^{*}$-algebras  of $tsr\ 1$.

AMSclassification. 17C65, 46H70, 46L70

Keywords. $C^{*}$-algebras, Jordan algebras, $JB^{*}$-algebras, unitary isotopes.