Dissertation
Eventual Cone Invariance
Doctor of Philosophy (PhD), Washington State University
01/2017
Handle:
https://hdl.handle.net/2376/13001
Abstract
If $K$ is a proper cone in $\\RR^{n}$ some results in the theory of eventually (entrywise) nonnegative matrices have equivalent analogues in eventual $K$-invariance. We develop these analogues using the classical Perron-Frobenius theory for cone preserving maps. Using an ice-cream cone we demonstrate that unlike the entrywise nonnegative case of a matrix $A \\in \\m $, eventual cone invariance and eventual exponential cone invariance are not equivalent. The notions of inverse positivity of {\\em M-matrices}, {\\em M-type} and {\\em $M_{v}$-matrices} are extended to {\\em $M_{v,K}$-matrices (operators)}, that have the form $A = sI - B$, where $B$ is eventually $K$-nonnegative, that is, $B^{m}K \\subseteq K$ for all sufficiently large $m$. Eventual positivity of semigroups of linear operators on Banach spaces ordered by a cone can be investigated using resolvents or resolvent type operators constructed from the generators.
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Details
- Title
- Eventual Cone Invariance
- Creators
- Michael Kasigwa
- Contributors
- Michael Tsatsomeros (Advisor)Judith McDonald (Committee Member)Nikos Voulgarakis (Committee Member)
- Awarding Institution
- Washington State University
- Academic Unit
- Department of Mathematics and Statistics
- Theses and Dissertations
- Doctor of Philosophy (PhD), Washington State University
- Number of pages
- 62
- Identifiers
- 99900581826301842
- Language
- English
- Resource Type
- Dissertation