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Title: A unified approach to Banach-Stone theorem on spaces of differentiable functions under various norms
Authors: Ng, Hong Wai
Keywords: Science::Mathematics
Issue Date: 2021
Publisher: Nanyang Technological University
Source: Ng, H. W. (2021). A unified approach to Banach-Stone theorem on spaces of differentiable functions under various norms. Doctoral thesis, Nanyang Technological University, Singapore.
Abstract: 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.
DOI: 10.32657/10356/148685
Rights: This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0).
Fulltext Permission: open
Fulltext Availability: With Fulltext
Appears in Collections:SPMS Theses

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