Isometries of certain function spaces

Rough Isometries of Lipschitz Function Spaces

We show that rough isometries between metric spacesX,Y can be lifted to the spaces of real valued 1-Lipschitz functions over X and Y with supremum metric and apply this to their scaling limits. For the inverse, we show how rough isometries between X and Y can be reconstructed from structurally enriched rough isometries between their Lipschitz function spaces.

On Characterizations of Isometries on Function Spaces

Let X be a Banach space over C. Let T : X → X be an isometric isomorphism (an onto linear operator on X with |Tx| = |x| for all x ∈ X). When X is a Hilbert space, any perturbations of orthonormal basis of X give an isometric isomorphism on X. But, for non-Hilbertian space, one expects that an isometric isomorphism should be something special, and would like to find a characterization for T on s...

The Isometries of Some Function Spaces

On the dual of certain locally convex function spaces

In this paper, we first introduce some function spaces, with certain locally convex topologies, closely  related to the space of real-valued continuous functions on $X$,  where $X$ is a $C$-distinguished topological space. Then, we show that their dual spaces can be identified in a natural way with certain spaces of Radon measures.

Representability of Certain Function Spaces

LetCp(X) be the space of all continuous real-valued functions on a space X , with the topology of pointwise convergence. In this paper we show thatCp(X) is not domain representable unless X is discrete for a class of spaces that includes all pseudo-radial spaces and all generalized ordered spaces. This is a first step toward our conjecture that if X is completely regular, then Cp(X) is domain r...