A unified approach to Banach-Stone theorem on spaces of differentiable functions under various norms

• Main Author: Ng, Hong Wai
• Other Authors: Tang Wee Kee
• Format: Thesis-Doctor of Philosophy
• Language: English
• Published: Nanyang Technological University 2021
• Subjects: Science::Mathematics
• Online Access: https://hdl.handle.net/10356/148685
• Institution: Nanyang Technological University

The classical Banach-Stone Theorem asserts that the isometric structure of the space of real-valued continuous functions determines a compact Hausdorf space up to homeomorphism. There are various extensions and generalizations of the result in different contexts. One of them is to consider vector-valued differentiable function space endowed with different norms. Existing literatures utilized special geometrical properties of norms to obtain a variant of the result. However, their methods are restricted to the considered norms only. In this thesis, we developed a general framework, which provides a sufficient condition to obtain Banach- Stone Theorem for vector-valued differentiable function space. Then we applied the framework on two different norms, which generalized most norms considered in existing literatures. When restricting them to \ell^p-norms, where p in [1,infinity), we obtained a characterization of Banach-Stone Theorem.