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.

Keywords:

separating maps, disjointness preserving, vector-valued absolutely continuous functions, automatic continuity separating maps, disjointness preserving, vector-valued absolutely continuous functions, automatic continuity

MSC Classifications:

47B38, 46E15, 46E40, 46H40, 47B33 show english descriptions Operators on function spaces (general)
Banach spaces of continuous, differentiable or analytic functions
Spaces of vector- and operator-valued functions
Automatic continuity
Composition operators 47B38 - Operators on function spaces (general)
46E15 - Banach spaces of continuous, differentiable or analytic functions
46E40 - Spaces of vector- and operator-valued functions
46H40 - Automatic continuity
47B33 - Composition operators

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