2002/05/15 by Charles A. Akemann, Joel Anderson, Akemann, Charles A. +1
Mathematics · #47A12 #Advanced Operator Algebra Research #FOS: Mathematics #Holomorphic and Operator Theory #Operator Algebras (math.OA) #Spectral Theory in Mathematical Physics #math.OA #msc:47A12
paper · pdf · doi:10.48550/arxiv.math/0205177
24 pages LATEX 2e
arxiv created 2002/05/15 · openalex publication_date 2002/05/15 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Suppose that c is an operator on a Hilbert Space H such that the von Neumann algebra N generated by c is finite. Suppose that tau is a faithful normal tracial state on N. Let B denote the spectal scale of c with respect to tau. We show that the boundary of the numerical range of c is exactly the set of radial complex slopes on B at the origin. Further, we show that points on this boundary that lie in the numerical range are visible as line segments in the boundary of B. Also, line segments on the boundary which lie in the numerical range show up as faces of dimension two in the boundary of B. Finally, when c is normal, we prove that the point spectrum of c is exactly the set of complex slopes of 1-dimensional faces of B.