Numerical Ranges in II${}_1$ Factors

Abstract

In this paper, we generalize the notion of the $C$-numerical range of a matrix to operators in arbitrary tracial von Neumann algebras. For each self-adjoint operator $C$, the $C$-numerical range of such an operator is defined; it is a compact, convex subset of $\mathbb{C}$. We explicitly describe the $C$-numerical ranges of several operators and classes of operators.

21 pages

Cited by in corpus (2)

• Closed Convex Hulls of Unitary Orbits in C${}^{\ast }$-Algebras of Real Rank Zero
• Convexity of the orbit-closed $C$-numerical range and majorization