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Zeitschrift für Analysis und ihre Anwendungen

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Volume 19, Issue 1, 2000, pp. 3–12
DOI: 10.4171/ZAA/934

Published online: 2000-03-31

Geometry of Numerical Ranges in Locally $m$-Convex *-Algebras

Th. Chryssakis

In this paper we examine the symmetry of numerical ranges in a unital locally $m$-convex $C*$- algebra of a given element and its adjoint, with respect to a rotated real-axis, where the rotation angle depends on the value of the positive linear forms of the algebra (states) at the unit clement of the algebra.

Keywords: Numerical, $k$-numerical, matrix numerical and Bonsai numerical ranges, $k$-states, locally $m$-convex, *- and C-algebras, *-representations

Chryssakis Th.: Geometry of Numerical Ranges in Locally $m$-Convex *-Algebras. Z. Anal. Anwend. 19 (2000), 3-12. doi: 10.4171/ZAA/934