APPROXIMATION AND CONVEX DECOMPOSITION BY EXTREMALS AND THE λ-FUNCTION IN JBW*-TRIPLES
We establish new estimates to compute the λ-function of Aron and Lohman on the unit ball of a
JB*-triple. It is established that for every Brown–Pedersen quasi-invertible element a in a JB*-triple E, we have
dist(a, E(E1)) = max{1 − mq (a), ||a||− 1},
where E(E1) denotes the set of extreme points of the closed unit ball E1 of E. It is proved that
λ(a) = (1 + mq (a))/2, for every Brown–Pedersen quasi-invertible element a in E1, where mq (a)
is the square root of the quadratic conorm of a. For an element a in E1 which is not Brown–Pedersen quasi-invertible, we can only estimate that λ(a) ≤ 21 (1 − αq (a)). A complete description of the λ-function on the closed unit ball of every JBW*-triple is also provided, and as a consequence, we prove that every JBW*-triple satisfies the uniform λ-property.
We establish new estimates to compute the λ-function of Aron and Lohman on the unit ball of a
JB*-triple. It is established that for every Brown–Pedersen quasi-invertible element a in a JB*-…
We introduce and study the class of extremally rich JB∗-triples. We establish new results to determine the distance from an element a in an extremally rich JB∗-triple E to the set ∂e(E1) of all…
The aim of this note is to study Cebyšëv JB*-subtriples of general JB*-triples. It is established that if F is a non-zero Cebyšëv JB*-subtriple of a JB*-triple E, then exactly one of the following…