Nonlinear diameter preserving maps on function spaces

Abstract

In this paper we study nonlinear diameter preserving mappings defined between function spaces and obtain generalizations of, basically, all known results concerning diameter preservers. In particular, we give a complete description for algebras of continuously differentiable functions, (little) Lipschitz algebras and dense function spaces.

Mathematics Subject Classification (2010): Primary 47B38; Secondary 46J10, 47B33.

Keywords: Diameter preserving maps, function spaces, function algebras, Choquet boundary, extreme point