Isometries on spaces of absolutely continuous functions in a noncompact framework

Absolutely Continuous Functions with Values in Metric Spaces

(see e.g. [1, Lemma 1.1]), we could without any loss of generality work with Banach spaces only. The main obstacle in dealing with metric spaces (or arbitrary Banach spaces) is the absence of the Radon-Nikodým property and the resulting non-existence of derivatives. Thus, instead of the “usual” derivative, we have to employ the notion of a “metric derivative” (which was introduced by Kirchheim ...

Linear Isometries between Subspaces of Continuous Functions

We say that a linear subspace A of C0(X) is strongly separating if given any pair of distinct points x1, x2 of the locally compact space X, then there exists f ∈ A such that |f(x1)| 6= |f(x2)|. In this paper we prove that a linear isometry T of A onto such a subspace B of C0(Y ) induces a homeomorphism h between two certain singular subspaces of the Shilov boundaries of B and A, sending the Cho...

Isometries on Spaces of Vector Valued Lipschitz Functions

This paper gives a characterization of a class of surjective isometries on spaces of Lipschitz functions with values in a finite dimensional complex Hilbert space.

Additive functionals on spaces with non-absolutely-continuous norm

On Absolutely Continuous Transformations