Linear biseparating maps between spaces of vector-valued differentiable functions and automatic continuity
Copyright policy )Linear biseparating maps between spaces of vector-valued differentiable functions and automatic continuity
In this paper, the maps called biseparating coincide with disjointness preserving mappings whose inverses preserve disjointness, too. The author characterizes all biseparating linear maps between the spaces of differentiable functions as weighted composition bijective maps. If the spaces are endowed with some topologies compatible with pointwise convergence, then the linear biseparating maps are continuous. The author gives a complete description of linear biseparating maps between spaces of vector-valued differentiable functions. Finally, some related questions concerning special cases are considered.
- University of Cantabria Spain
Biseparating map, Disjointness preserving, Mathematics(all), automatic continuity, vector-valued differentiable functions, Linear composition operators, biseparating maps, Rings and algebras of continuous, differentiable or analytic functions, Vector-valued differentiable functions, Spaces of vector- and operator-valued functions, Linear operators on function spaces (general), Automatic continuity
Biseparating map, Disjointness preserving, Mathematics(all), automatic continuity, vector-valued differentiable functions, Linear composition operators, biseparating maps, Rings and algebras of continuous, differentiable or analytic functions, Vector-valued differentiable functions, Spaces of vector- and operator-valued functions, Linear operators on function spaces (general), Automatic continuity
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