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Hyperreflexivity of von Neumann algebras and similarity of finitely generated C^*-algebras

2025/05/13 by George Eleftherakis, Vern I. Paulsen, Eleftherakis, G. K. +1
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.2505.08720

openalex publication_date 2025/05/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let A be a C^*-algebra. We say that A satisfies the SP if every bounded homomorphism A→ B(K), with K a Hilbert space, is similar to a *-homomorphism. We introduce three hypotheses that relate to extending hyperreflexive algebras by projections. We prove that our third hypothesis is equivalent to every finitely generated C*-algebra satisfying the SP. We show that to prove that every von Neumann algebra is hyperreflexive it is enough to show that when one extends a hyperreflexive algebra by a single projection it remains hyperreflexive.

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