Isometries and approximate local isometries between AC^p(X)-spaces
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2022-07-29Abstract
Let X and Y be compact subsets of R with at least two points. For p ≥ 1, let AC^p(X) be the space of all absolutely continuous complex-valued functions f on X such that f' in L^p(X), with the sum norm. e describe the topological reflexive closure of the set of linear isometries from AC^p(X) onto AC^p(Y ). Using this description, we prove that such a set is algebraically reflexive and 2-algebraically reflexive. Moreover, as another application, it is shown that the sets of isometric reflections and generalized bi-circular projections of AC^p(X) are topologically reflexive and 2-topologically reflexive.
Palabra/s clave
Surjective linear isometry
Algebraic reflexivity
Topological reflexivity
Local isometry
2-Local isometry
Absolutely continuous function
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