Diameter-preserving maps on various classes of function spaces

Tom 153 / 2002

Bruce A. Barnes, Ashoke K. Roy Studia Mathematica 153 (2002), 127-145 MSC: Primary 46E25, 46A55, 47B38, 52A41. DOI: 10.4064/sm153-2-3


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.


  • Bruce A. BarnesDepartment of Mathematics
    University of Oregon
    Eugene, OR 97403, U.S.A.
  • Ashoke K. RoyIndian Statistical Institute–Calcutta
    Statistics and Mathematics Unit
    203 B. T. Road
    Calcutta 700 035, India

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