JOURNAL BROWSE
Search
Advanced SearchSearch Tips
 HOME > Journal Browse > About Journal > Journal Vol & Issue > Full Record
ON DIAMETER PRESERVING LINEAR MAPS
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
ON DIAMETER PRESERVING LINEAR MAPS
Aizpuru, Antonio; Tamayo, Montserrat;
  PDF(new window)
 Abstract
We study diameter preserving linear maps from C(X) into C(Y) where X and Y are compact Hausdorff spaces. By using the extreme points of and a linear condition on them, we obtain that there exists a diameter preserving linear map from C(X) into C(Y) if and only if X is homeomorphic to a subspace of Y. We also consider the case when X and Y are noncompact but locally compact spaces.
 Keywords
diameter preserving map;extreme point;locally compact space;
 Language
English
 Cited by
3time(s) in CrossRef
1.
Diameter preserving maps on function spaces, Positivity, 2017, 21, 3, 875  crossref(new windwow)
2.
Linear bijections which preserve the diameter of vector-valued maps, Linear Algebra and its Applications, 2007, 424, 2-3, 371  crossref(new windwow)
3.
Nonlinear Diameter Preserving Maps Between Certain Function Spaces, Mediterranean Journal of Mathematics, 2016, 13, 6, 4237  crossref(new windwow)
 References
1.
A. Aizpuru and F. Rambla, There's something about the diameter, J. Math. Anal. Appl. 330 (2007), no. 2, 949-962. crossref(new window)

2.
B. A. Barnes and A. K. Roy, Diameter preserving maps on various classes of function spaces, Studia Math. 153 (2002), no. 2, 127-145 crossref(new window)

3.
F. Cabello Sanchez, Diameter preserving linear maps and isometries, Arch. Math. (Basel) 73 (1999), no. 5, 373-379. crossref(new window)

4.
J. J. Font and M. Sanchıs, A characterization of locally compact spaces with homeomorphic one-point compactifications, Topology Appl. 121 (2002), 91-104 crossref(new window)

5.
F. Gonzalez and V. V. Uspenkij, On homeomorphisms of groups of integer-valued functions, Extracta Math. 14 (1999), no. 1, 19-29.

6.
M. Gyory and L. Molnar, Diameter preserving linear bijections of C(X), Arch. Math. 71 (1998), 301-310 crossref(new window)

7.
W. Holsztynski, Continuous mappings induced by isometries of spaces of continuous functions, Studia Math. 26 (1966), 133-136

8.
J. S. Jeang and N. C. Wong, On the Banach-Stone problem, Studia Math. 155 (2003), no. 2, 95-105 crossref(new window)

9.
A. Moreno-Galindo and A. Rodriguez-Palacios, A bilinear version of Holsztynski's theorem on isometries of C(X)-spaces, Studia Math. 166 (2005), no. 1, 83-91 crossref(new window)

KISTIKorea Institute of Science and Technology Information Contact to : koreascience@kisti.re.kr Copyright@2012 KISTI All Rights Reserved. For more information mail to webmaster.