Relations amongst the distances between C^*-subalgebras and some canonically associated operator algebras

2025/01/22 by Ved Prakash Gupta, Sumit Kumar, Gupta, Ved Prakash +1
Computer Science · Mathematics · #46L05 #46M05 #47L40 #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Matrix Theory and Algorithms #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.2501.13039

openalex publication_date 2025/01/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that the Christensen distance (resp., the Kadison-Kastler distance) between two C^*-subalgebras A and B of a C^*-algebra C is equal to that between their enveloping von Neumann algebras A^** and B^** (resp., the tensor product algebras A ⊗^min D and B ⊗^min D, for any unital commutative C^*-algebra D).

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