Please use this identifier to cite or link to this item: https://hdl.handle.net/10356/148685
 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. https://hdl.handle.net/10356/148685 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. URI: https://hdl.handle.net/10356/148685 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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