Keywords
projectional skeleton, biorthogonal system, PRI, density character, norming subspaces, Hamel basis
Abstract
This paper studies Markushevich bases and Auerbach bases in Banach spaces. Firstly, a countable 1-norming Markushevich basis is constructed for any infinite-dimensional separable Banach space. Secondly, an Auerbach basis is constructed for any finite-dimensional Banach space. Thirdly, a Markushevich basis is constructed for a class of non-separable Banach spaces by applying projectional generators and projectional resolution identities, and the transfinite induction on the density character of the space.
Primary Advisor
Zhiguo Hu
Program Reader
Dilian Yang
Degree Name
Master of Science
Department
Mathematics and Statistics
Document Type
Major Research Paper
Convocation Year
2022
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.