The λ-function in JB⁎-triples

We discuss the λ-function in the general setting of JB⁎-triples. Several results connecting the λ-function with the distance of a vector to the Brown-Pedersen's quasi-invertible elements and extreme convex decompositions have been obtained for JB⁎-triples; these include JB⁎-triple analogues of some related C⁎-algebra results due to M. Rørdam, L. Brown and G. Pedersen.