Diameter-preserving maps on various classes of function spaces

• Autorzy: Bruce A. Barnes , Ashoke K. Roy
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 47B38: Operators on function spaces (general)
• 46A55: Convex sets in topological linear spaces; Choquet theory
• 52A41: Convex functions and convex programs
• 46E25: Rings and algebras of continuous, differentiable or analytic functions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2002
• Tom: 153
• Numer: 2
• Strony: 127-145

Daty

wydano

2002

Twórcy

autor

Bruce A. Barnes

• Department of Mathematics, University of Oregon, Eugene, OR 97403, U.S.A.

autor

Ashoke K. Roy

• Indian Statistical Institute-Calcutta, Statistics and Mathematics Unit, 203 B. T. Road, Calcutta 700 035, India

Identyfikatory

DOI

10.4064/sm153-2-3