Work

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

Year: 2026

Type: article

Abstract: 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 → 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.

Source: Integral Equations and Operator Theory

DOI: 10.1007/s00020-026-02832-2

Authors: G. K. Eleftherakis, V. I. Paulsen

Institutions: University of Patras, University of Waterloo

Language: English

Topic: Advanced Operator Algebra Research

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,290

Funder: University of Patras