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. Rørdam ar
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