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Banach–Stone theorems for spaces of vector bundle continuous sections

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Abstract We prove Banach–Stone type theorems for linear isometries on spaces of continuous sections of Banach space bundles. These extend a previous result for vector-valued continuous function spaces. Two common… Click to show full abstract

Abstract We prove Banach–Stone type theorems for linear isometries on spaces of continuous sections of Banach space bundles. These extend a previous result for vector-valued continuous function spaces. Two common methods, examining the extreme point sets of the dual spaces and examining peak points, are adopted to prove two similar but slightly different theorems.

Keywords: theorems spaces; continuous sections; stone theorems; banach stone; sections banach

Journal Title: Topology and its Applications
Year Published: 2017

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