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arXiv · 2505.08720

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

G. K. Eleftherakis·V. I. Paulsen
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Abstract

Let $A$ be a $C^*$-algebra. We say that $A$ satisfies the SP if every bounded homomorphism $A\to B(K)$, 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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BibTeXRIS

G. K. Eleftherakis, V. I. Paulsen. 2025-05-13. Hyperreflexivity of von Neumann algebras and similarity of finitely generated $C^*$-algebras. https://arxiv.org/abs/2505.08720

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