Metric characterisation of unitaries in JB^*-algebras

2019/07/10 by María Cueto-Avellaneda, Cueto-Avellaneda, María, Antonio M. Peralta +1 · 1 citation
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.1907.04738

openalex publication_date 2019/07/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let M be a unital JB^*-algebra whose closed unit ball is denoted by B_M. Let ∂_e(B_M) denote the set of all extreme points of B_M. We prove that an element u∈ ∂_e(B_M) is a unitary if and only if the set M_u = \e∈ ∂_e(B_M) : ‖u± e‖≤ √(2) \ contains an isolated point. This is a new geometric characterisation of unitaries in M in terms of the set of extreme points of B_M.

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