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<p>A geometric commutation principle in Euclidean Jordan algebras, recently proved by Gowda, says that for any spectral set <i>E</i> in a Euclidean Jordan algebra <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathcal {V}\)</EquationSource> </InlineEquation> and <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(a \in E\)</EquationSource> </InlineEquation>, <i>a</i> strongly operator commutes with every element in the normal cone <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(N_E(a)\)</EquationSource> </InlineEquation>. Further, it can be used to establish strong operator commutativity relations in certain optimization problems. Knowing that every spectral set is a member of a broader class of weakly spectral sets, we prove an analog of a geometric commutation principle for weakly spectral sets in terms of operator commutativity and study its consequences and applications.</p>

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Geometric commutation principles for weakly spectral sets in Euclidean Jordan algebras

  • 期刊论文

  • 发表日期：

    2025年9月24日

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  • Juyoung Jeong

摘要

A geometric commutation principle in Euclidean Jordan algebras, recently proved by Gowda, says that for any spectral set E in a Euclidean Jordan algebra \(\mathcal {V}\) and \(a \in E\) , 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 set is a member of a broader class of weakly spectral sets, we prove an analog of a geometric commutation principle for weakly spectral sets in terms of operator commutativity and study its consequences and applications.