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

Abstract

In this paper we examine the symmetry of numerical ranges in a unital locally $m$-convex $C\ast$- 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.