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Numerical Ranges in II1 Factors

Part of: Selfadjoint operator algebras Individual linear operators as elements of algebraic systems Basic linear algebra General theory of linear operators

Published online by Cambridge University Press:  16 March 2017

Ken Dykema  and
Paul Skoufranis
Ken Dykema*
Affiliation:
Department of Mathematics, Texas A&M University, College Station, TX 77843, USA (kdykema@math.tamu.edu; pskoufra@math.tamu.edu)
Paul Skoufranis*
Affiliation:
Department of Mathematics, Texas A&M University, College Station, TX 77843, USA (kdykema@math.tamu.edu; pskoufra@math.tamu.edu)
*
*Corresponding author.
*Corresponding author.
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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 ℂ. We explicitly describe the C-numerical ranges of several operators and classes of operators.

Keywords

II1 FactorsNumerical RangeGeneralized Numerical Range

MSC classification

Primary: 46L10: General theory of von Neumann algebras 47C15: Operators in $C^*$- or von Neumann algebras 47A12: Numerical range, numerical radius 15A60: Norms of matrices, numerical range, applications of functional analysis to matrix theory
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 61 , Issue 1 , February 2018 , pp. 31 - 55
Copyright
Copyright © Edinburgh Mathematical Society 2018 

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