Positivity (2017) 21:875–883
Diameter preserving maps on function spaces
· Juan J. Font
Received: 23 October 2014 / Accepted: 9 August 2016 / Published online: 16 August 2016
© Springer International Publishing 2016
Abstract In this paper we describe, under certain assumptions, surjective diameter
preserving mappings when deﬁned between function spaces, not necessarily algebras,
thus extending most of the previous results for these operators. We provide an example
which shows that our assumptions are not redundant.
Keywords Diameter-preserving maps · Function spaces · Choquet boundary
Mathematics Subject Classiﬁcation Primary 47B38; Secondary 46J10 · 47B33
1 Introduction and preliminaries
In 1998, Gy˝ory and Molnár  introduced a new kind of linear operators based on
the preservation of the diameter of the range of the functions. Since then, several
papers have been published extending the scope of application of diameter preserving
mappings (see e.g., [1–4,7–9,13,15,18]).
Diameter preserving mappings are indeed isometries if we consider the underlying
spaces of functions endowed with the diameter (semi) norm. So, it is apparent that
Research of J.J. Font was partially supported by Universitat Jaume I (Projecte P1·1B2014-35) and
Generalitat Valenciana (Projecte AICO/16/030).
Juan J. Font
Department of Mathematics, K.N. Toosi University of Technology, 16315-1618, Tehran, Iran
Departament de Matemàtiques, and Institut Universitari de Matemàtiques i Aplicacions de Castelló
(IMAC), Universitat Jaume I, Campus del Riu Sec. s/n, 12071 Castellón, Spain