Geodesic
Diameter-preserving maps on various classes of function spaces
Bruce A. Barnes1 ; Ashoke K. Roy2
1 Department of Mathematics University of Oregon Eugene, OR 97403, U.S.A.
2 Indian Statistical Institute–Calcutta Statistics and Mathematics Unit 203 B. T. Road Calcutta 700 035, India
Studia Mathematica, Tome 153 (2002) no. 2, pp. 127-145 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/sm153-2-3
Keywords: under mild assumptions non linear diameter preserving bijections between vector valued function spaces characterized help well known theorem ulam mazur necessary sufficient condition existence diameter preserving bijection between function spaces complex scalar derived complete description maps given several important cases

Bruce A. Barnes 1 ; Ashoke K. Roy 2

1 Department of Mathematics University of Oregon Eugene, OR 97403, U.S.A.
2 Indian Statistical Institute–Calcutta Statistics and Mathematics Unit 203 B. T. Road Calcutta 700 035, India 
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Bruce A. Barnes; Ashoke K. Roy. Diameter-preserving maps on various classes
 of function spaces. Studia Mathematica, Tome 153 (2002) no. 2, pp. 127-145. doi: 10.4064/sm153-2-3

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