Abstract
We study linear bijections of simplex spacesA(S) which preserve the diameter of the range, that is, the seminorm ϱ(f)=sup{|f(x)−f(y)|:x,yεS}.
Similar content being viewed by others
References
Alfsen E M, Compact convex sets and boundary integrals,Ergebnisse der Math. 57 (Springer) (1971)
Cabello Sánchez F, Diameter preserving linear maps and isometries,Arch. Math. (Basel) 73 (1999) 373–379
González F and Uspenskij V V, On homomorphisms of groups of integer-valued functions,Extraeta Math. 14 (1999) 19–29
Györy M and Molnár L, Diameter preserving linear bijections ofC(X),Arch. Math. (Basel) 71 (1998) 301–310
Li C-K and Tsing N-K, Linear preserver problems: a brief introduction and some special techniques,Linear Algebra Appl. 162-164 (1992) 217–235
Lindenstrauss J, Some useful facts about Banach spaces, (Springer Lecture Notes in Mathematics) 1317
Poulsen E T, A simplex with dense extreme boundary,Ann. Inst. Fourier 11 (1961) 83–87
Rao T S S R K and Roy A K, Diameter preserving linear bijections of function spaces (preprint 1999)
Semadeni Z, Banach Spaces of Continuous Functions,Monografie Matematyczne 55 (1971) PWN
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Sánchez, F.C. Diameter preserving linear maps and isometries, II. Proc. Indian Acad. Sci. (Math. Sci.) 110, 205–211 (2000). https://doi.org/10.1007/BF02829491
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02829491