An octagon containing the numerical range of a bounded linear operator

02/08/2021

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by   Aaron Melman, et al.

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A polygon is derived that contains the numerical range of a bounded linear operator on a complex Hilbert space, using only norms. In its most general form, the polygon is an octagon, symmetric with respect to the origin, and tangent to the closure of the numerical range in at least four points when the spectral norm is used.