Topological properties of spaces of ideals of the minimal tensor product

2009/06/16 by Aldo J. Lazar, Lazar, Aldo J. · 1 citation
Mathematics · #46L06 #Advanced Banach Space Theory #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Operator Algebras (math.OA) #math.OA #msc:46L06

paper · pdf · doi:10.48550/arxiv.0906.2896

7 pages

arxiv created 2009/06/16 · openalex publication_date 2009/06/16 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

One shows that for two C^*-algebras A₁ and A₂ any continuous function on Prim(A₁)× Prim(A₂) can be continuously extended to Prim(A₁⊗ A₂) provided it takes its values in a T₁ topological space. This generalizes a 1977 result of L.G. Brown. A new proof is given for a result of R.J. Archbold about the space of minimal primal ideals of A₁⊗ A₂. To obtain these two results one makes use of the topological properties of the space of prime ideals of the minimal tensor product.

Cited by

• Ideal Spaces of the Haagerup Tensor Product of Ternary Rings of Operators

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