2006/11/17 by Kenley Jung, Jung, Kenley
Mathematics · #46L54 #52C17 #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #FOS: Mathematics #Operator Algebras (math.OA) #Random Matrices and Applications
paper · pdf · doi:10.48550/arxiv.math/0611536
openalex publication_date 2006/11/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let M be a tracial von Neumann algebra and A be a weakly dense unital C*-subalgebra of M. We say that a set X is a W*-generating set for M if the von Neumann algebra generated by X is M and that X is a C*-generating set for A if the unital C*-algebra generated by X is A. For any finite W*-generating set X for M we show that δ0(X) ≤ sup δ0(Y): Y is a finite C*-generating set for A where δ0 denotes the microstates free entropy dimension. It follows that if sup δ0(Y): Y is a finite C*-generating set for C*red(\mathbb F2) < ∞, then the free group factors are all nonisomorphic.