The Hyperrigidity Conjecture for compact convex sets in ℝ²

2024/11/18 by Marcel Scherer, Scherer, Marcel · 1 citation
Computer Science · Mathematics · #46L07 #47B15 #Advanced Optimization Algorithms Research #FOS: Mathematics #Functional Analysis (math.FA) #Optimization and Variational Analysis #Primary 46L05

paper · pdf · doi:10.48550/arxiv.2411.11709

openalex publication_date 2024/11/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that for every compact, convex subset K⊂ℝ² the operator system A(K), consisting of all continuous affine functions on K, is hyperrigid in the C*-algebra C(ex(K)). In particular, this result implies that the weak and strong operator topologies coincide on the set \ T\inB(H); T normal and σ(T)⊂ ex(K) \. Our approach relies on geometric properties of K and generalizes previous results by Brown.

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• A new obstruction to Arveson's hyperrigidity conjecture

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