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Computability-theoretic complexity of effective Banach spaces

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thesis
posted on 09.01.2022, 21:13 by Qian, Long

We 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

Advisor 1

Downey, Rod

Advisor 2

Greenberg, Noam

Copyright Date

27/12/2021

Date of Award

27/12/2021

Publisher

Victoria University of Wellington - Te Herenga Waka

Rights License

CC BY-SA 4.0

Degree Discipline

Mathematics

Degree Grantor

Victoria University of Wellington - Te Herenga Waka

Degree Level

Masters

Degree Name

Master of Science

ANZSRC Type Of Activity code

1 PURE BASIC RESEARCH

Victoria University of Wellington Item Type

Awarded Research Masters Thesis

Language

en_NZ

Victoria University of Wellington School

School of Mathematics and Statistics

Advisors

Downey, Rod; Greenberg, Noam