Izomorfní vlastnosti prostorů spojitých afinních funkcí

Abstract

The thesis deals with Banach-Stone theorem, its modi cations and generalizations. The preface of the thesis contains a lot of well known results and useful assertions from such elds of mathematics as measury theory, functional analysis, topology and most importantly convex analysis. The second chapter pursues proofs of classical Banach-Stone theorem and Eilenberg theorem, which works in another context than the original theorem. Chapter number three contains contribution of A. Lazar, who proved variation of Banach-Stone theorem for afine functions on simplexes. The chapter follows with generalizations of his results and it is closed with our own slight generalization. The last chapter pays attention to "almost isometries". The chapter comes out from theorem proved by A. Amir and continues with improvements achieved by H.B. Cohen and C.-H. Chu. The last part includes our own contribution to the subject.