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Computability-theoretic complexity of effective Banach spaces
thesis
posted on 2022-01-09, 21:13 authored by Qian, LongWe investigate the geometry of effective Banach spaces, namely a sequenceof approximation properties that lies in between a Banach space having a basis and the approximation property.
We establish some upper bounds on suchproperties, as well as proving some arithmetical lower bounds. Unfortunately,the upper bounds obtained in some cases are far away from the lower bound.
However, we will show that much tighter bounds will require genuinely newconstructions, and resolve long-standing open problems in Banach space theory.
We also investigate the effectivisations of certain classical theorems in Banachspaces.
History
Copyright Date
2021-12-27Date of Award
2021-12-27Publisher
Te Herenga Waka—Victoria University of WellingtonRights License
CC BY-SA 4.0Degree Discipline
MathematicsDegree Grantor
Te Herenga Waka—Victoria University of WellingtonDegree Level
MastersDegree Name
Master of ScienceANZSRC Type Of Activity code
1 PURE BASIC RESEARCHVictoria University of Wellington Item Type
Awarded Research Masters ThesisLanguage
en_NZVictoria University of Wellington School
School of Mathematics and StatisticsAdvisors
Downey, Rod; Greenberg, NoamUsage metrics
Keywords
ClassificationBanach spacesComputable analysisSchool: School of Mathematics and Statistics010107 Mathematical Logic, Set Theory, Lattices and Universal AlgebraDegree Discipline: MathematicsDegree Level: MastersDegree Name: Master of ScienceMathematical Logic, Set Theory, Lattices and Universal Algebra
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