Realcompactness and Banach-Stone theorems

2000/10/30 by Jesus Araujo, Araujo, Jesus
Mathematics · #46E40 (Primary) 47B33 #47B38 #54D60 (Secondary) #FOS: Mathematics #Functional Analysis (math.FA) #General Topology (math.GN) #math.FA #math.GN #msc:46E40 #msc:47B33 #msc:47B38 #msc:54D60

paper · pdf · doi:10.48550/arxiv.math/0010292

14 pages, LaTeX, no figures. Changes in introduction. In section 2 results valid for normed spaces instead of Banach spaces

arxiv created 2001/05/14 · arxiv updated 2009/11/30

Abstract

For realcompact spaces X and Y we give a complete description of the linear biseparating maps between spaces of vector-valued continuous functions on X and Y, where special attention is paid to spaces of vector-valued bounded continuous functions. These results are applied to describe the linear isometries between spaces of vector-valued bounded continuous and uniformly continuous functions.

Related

• Realcompactness and spaces of vector-valued functions
• Separating maps between spaces of vector-valued absolutely continuous functions
• Automatic continuity of biseparating maps
• Automatic continuity and weighted composition operators between spaces of vector-valued differentiable functions
• Isometries between weighted uniform spaces