Geometric commutation principle for weakly spectral sets in Euclidean Jordan algebras

2024/09/07 by Juyoung Jeong, Jeong, Juyoung
Computer Science · Mathematics · #17C20 #17C30 #52A41 #90C26 #Advanced Topics in Algebra #FOS: Mathematics #Matrix Theory and Algorithms #Optimization and Control (math.OC)

paper · pdf · doi:10.48550/arxiv.2409.04712

openalex publication_date 2024/09/07 · openalex created_date 2024/10/22 · openalex updated_date 2026/07/28

Abstract

A geometric commutation principle in Euclidean Jordan algebra, recently proved by Gowda, says that, for any spectral set E in a Euclidean Jordan algebra V and a ∈ E, a strongly operator commutes with every element in the normal cone N_E(a). Further, it can be used to establish strong operator commutativity relations in certain optimization problems. Knowing that every spectral sets are special cases of broader class of weakly spectral sets, we prove an analog of a geometric commutation principle for weakly spectral sets and study its consequences and applications.

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