Separating maps between spaces of vector-valued absolutely continuous functions

2009/06/09 by Luis Dubarbie, Dubarbie, Luis
Mathematics · #46E15 #46E40 #46H40 #47B33 #47B38 #FOS: Mathematics #Functional Analysis (math.FA) #math.FA #msc:46E15 #msc:46E40 #msc:46H40 #msc:47B33 #msc:47B38

paper · pdf · doi:10.48550/arxiv.0906.1633

Canadian Mathematical Bulletin, to appear

arxiv created 2009/06/09 · arxiv updated 2009/12/01

Abstract

In this paper we give a description of separating or disjointness preserving linear bijections on spaces of vector-valued absolutely continuous functions defined on compact subsets of the real line. We obtain that they are continuous and biseparating in the finite-dimensional case. The infinite-dimensional case is also studied.

Related

• Automatic continuity of biseparating maps
• Realcompactness and Banach-Stone theorems
• Nonlinear biseparating maps
• Automatic continuity and weighted composition operators between spaces of vector-valued differentiable functions
• Maps preserving common zeros between subspaces of vector-valued continuous functions