Hyperreflexivity of Von Neumann Algebras and Similarity of Finitely Generated $C^*$-Algebras

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2026年3月26日

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G. K. Eleftherakis,
V. I. Paulsen

摘要

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

Hyperreflexivity of Von Neumann Algebras and Similarity of Finitely Generated \(C^*\)-Algebras

摘要