In unital JB*-algebras, an extreme point u of the closed unit ball is unitary if and only if the set of extreme points e with ||u ± e|| ≤ √2 contains an isolated point.
Fern´ andez-Polo, A.M
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Metric characterisation of unitaries in JB$^*$-algebras
In unital JB*-algebras, an extreme point u of the closed unit ball is unitary if and only if the set of extreme points e with ||u ± e|| ≤ √2 contains an isolated point.