4 papers · 1 filter
Automatic continuity of biseparating maps
Jesus Araujo, Krzysztof Jarosz
We prove that a biseparating map between spaces of vector-valued continuous functions is usually automatically continuous. However, we also discuss special cases when it is not tru…
Isometric shifts and metric spaces
Jesus Araujo, Juan J. Font
Let M be a complete metric space. It is proved that if the space or scalar-valued bounded continuous functions on M admits an isometric shift, then M is separable.
Automatic continuity and weighted composition operators between spaces of vector-valued differentiable functions
Jesus Araujo
It is proved that every linear biseparating map between spaces of vector-valued differentiable functions is a weighted composition map. As a consequence, such a map is always conti…
Realcompactness and Banach-Stone theorems
Jesus Araujo
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 attenti…