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.

In 1976, Kaplansky introduced the class JB∗-algebras which includes all C∗-algebras as a proper subclass. The notion of topological stable rank 1 for C∗-algebras was originally introduced by M. A. Rieffel and was extensively studied by various authors. In this paper, we extend this notion to general JB∗-algebras. We show that the complex spin factors are of tsr 1 providing an example of special...

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

We continue our recent efforts to exploit the notion of a unitary isotope to study convex combinations of unitaries in an arbitrary JB∗-algebra. Exact analogues of C∗-algebraic results, due to R. V. Kadison, C. L. Olsen and G. K. Pedersen, are proved for general JB∗-algebras. We show that if a contraction in a JB∗-algebra is a convex combination of n unitaries, then it is also a mean of n unita...

We define type A, type B, type C as well as C∗-semi-finite C∗-algebras. It is shown that a von Neumann algebra is a type A, type B, type C or C∗-semi-finite C∗-algebra if and only if it is, respectively, a type I, type II, type III or semi-finite von Neumann algebra. Moreover, any type I C∗-algebra is of type A (actually, type A coincides with the discreteness as defined by Peligrad and Zsidó),...

It has been established by Inoue that a complex locally C*-algebra with a dense ideal posesses a bounded approximate identity which belonges to that ideal. It has been shown by Fritzsche that if a unital complex locally C*-algebra has an unbounded element then it also has a dense one-sided ideal. In the present paper we obtain analogues of the aforementioned results of Inoue and Fritzsche for r...

We study transitivity conditions on the norm of JB∗-triples, C∗-algebras, JBalgebras, and their preduals. We show that, for the predual X of a JBW∗-triple, each one of the following conditions i) and ii) implies that X is a Hilbert space. i) The closed unit ball of X has some extreme point and the norm of X is convex transitive. ii) The set of all extreme points of the closed unit ball of X is ...

Working at the level of Poisson brackets, we describe the extension of the generalized Wakimoto realization of a simple Lie algebra valued current, J, to a corresponding realization of a group valued chiral primary field, b, that has diagonal monodromy and satisfies Kb ′ = Jb. The chiral WZNW field b is subject to a monodromy dependent exchange algebra, whose derivation is reviewed, too.

Working at the level of Poisson brackets, we describe the extension of the generalized Wakimoto realization of a simple Lie algebra valued current, J, to a corresponding realization of a group valued chiral primary field, b, that has diagonal monodromy and satisfies Kb ′ = Jb. The chiral WZNW field b is subject to a monodromy dependent exchange algebra, whose derivation is reviewed, too.