Please use this identifier to cite or link to this item: http://scholarbank.nus.edu.sg/handle/10635/144266
Title: NON-LINEAR BISEPARATING OPERATORS ON VECTOR-VALUED FUNCTION SPACES
Authors: FENG XIANZHE
Keywords: Nonlinear biseparating operators, continuous functions, uniformly continuous functions, Lipschitz functions, differentiable functions, Banach spaces
Issue Date: 24-Jan-2018
Citation: FENG XIANZHE (2018-01-24). NON-LINEAR BISEPARATING OPERATORS ON VECTOR-VALUED FUNCTION SPACES. ScholarBank@NUS Repository.
Abstract: In my thesis, I first proved that a non-linear biseparating operator between a class of function spaces induces a bijection between a class of open sets. Such bijection will further induce a homeomorphism between the underlying spaces X and Y when they are both realcompact, or metric spaces. Next, I obtained the functional representation of non-linear biseparating operators, i.e., they must take the form of weight composition operators. After that, I applied the functional representation and obtained characterizations of non-linear biseparating operators between various classes of function spaces, such as continuous, uniformly continuous, Lipschitz continuous and differentiable function spaces.
URI: http://scholarbank.nus.edu.sg/handle/10635/144266
Appears in Collections:Ph.D Theses (Open)

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