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Numerical Ranges in II1 Factors

Published online by Cambridge University Press:  16 March 2017

Ken Dykema*
Affiliation:
Department of Mathematics, Texas A&M University, College Station, TX 77843, USA ([email protected]; [email protected])
Paul Skoufranis*
Affiliation:
Department of Mathematics, Texas A&M University, College Station, TX 77843, USA ([email protected]; [email protected])
*
*Corresponding author.
*Corresponding author.

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.

Type
Research Article
Copyright
Copyright © Edinburgh Mathematical Society 2018 

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