Major Papers

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

Included in

Analysis Commons

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