A Symmetric Numerical Range for Matrices
نویسندگان
چکیده
For each norm v on <en, we define a numerical range Z., which is symmetric in the sense that Z. =Z"D, where vD is the dual norm. We prove that, for aE <enn, Z.(a) contains the classical field of values V(a). In the special case that v is the lcnorm, Z.(a) is contained in a set G(a) of Gershgorin type defined by C. R. Johnson. When a is in the complex linear span of both the Hennitians and the v-Hennitians, then Z.(a), V(a) and the convex hull of the usual v-numerical range V.(a) all coincide. We prove some results concerning points of V(a) which are extreme points of Z.(a).
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