Date of Award

1-1-2019

Language

English

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

College/School/Department

Department of Mathematics and Statistics

Content Description

1 online resource (vi, 54 pages) : illustrations.

Dissertation/Thesis Chair

Rongwei Yang

Committee Members

Michael Stessin, Kehe Zhu, Hyun-Kyoung Kwon

Keywords

Extremal Equation, Functional Analysis, Geometry, Nilpotent Operator, Resolvent Set, Unilateral Shift Operator, Resolvents (Mathematics), Hilbert space, Functional analysis, Operator theory, Curvature

Subject Categories

Physical Sciences and Mathematics

Abstract

For a bounded linear operator $A$ on a complex Hilbert space $\mathcal{H}$, the Douglas-Yang metric on the resolvent set $\rho(A)$ is defined by the metric function $g_{\vec{x}}(z)=\left \| \big(A -z I\big)^{-1} \vec{x} \right \|^2$, where $\vec{x} \in \mathcal{H}$ with $\left \| \vec{x} \right \|=1$.

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