Diameter-preserving maps on various classes of function spaces
Volume 153 / 2002
Studia Mathematica 153 (2002), 127-145
MSC: Primary 46E25, 46A55, 47B38, 52A41.
DOI: 10.4064/sm153-2-3
Abstract
Under some mild assumptions, non-linear diameter-preserving bijections between (vector-valued) function spaces are characterized with the help of a well-known theorem of Ulam and Mazur. A necessary and sufficient condition for the existence of a diameter-preserving bijection between function spaces in the complex scalar case is derived, and a complete description of such maps is given in several important cases.
