Reflexivity of sets of isometries on bounded variation function spaces.

For arbitrary subsets X and Y of the real line with at least two points, let BV(X) (resp. BV(Y)) be the Banach space of all functions of bounded variation on X (resp. Y) endowed with the natural norm ‖ ⋅ ‖ ∞ + V (⋅) , where ‖ ⋅ ‖ ∞ and V (⋅) denote the supremum norm and the total variation of a function, respectively. We show that the set of all surjective linear isometries from BV(X) onto BV(Y) is topologically reflexive. Among the consequences, it is also proved that the set of all isometric reflections, and the set of all generalized bi-circular projections on BV(X) are topologically reflexive. [ABSTRACT FROM AUTHOR]