Operator Theory Seminar - Dylan Johnson; Department of Mathematics, University of Iowa

The numerical range of a Hilbert Space operator is a subset of the complex plane which contains information about the algebraic and norm properties of said operator. Classical results, including the Toeplitz-Hausdorff theorem will be presented. Two generalizations, the spatial numerical range and higher rank numerical range, will also be presented.

The numerical measure of a complex valued matrix is the measure induced by the matrix and its numerical range map. An overview of these measures and their properties will be explored.

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Operator Theory Seminar - Dylan Johnson; Department of Mathematics, University of Iowa

Overview of Numerical Range and Numerical Measure of Bounded Operators