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arXiv · 1503.05766

Numerical Ranges in II$_1$ Factors

Ken Dykema·Paul Skoufranis
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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.

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Ken Dykema, Paul Skoufranis. 2015-10-08. Numerical Ranges in II$_1$ Factors. https://doi.org/10.1017/s0013091516000572

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