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 $\left \| \vec{x} \right \|=1$.
Recommended Citation
Tran, Mai Thi Thuy, "Non-Euclidean metric on the resolvent set" (2019). Legacy Theses & Dissertations (2009 - 2024). 2400.
https://scholarsarchive.library.albany.edu/legacy-etd/2400