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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 C(X)* and C(Y)* 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.
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참고문헌 (9)
참고문헌 신청
A. Aizpuru / 2007 / There’s something about the diameter / Journal of Mathematical Analysis and Applications 330 (2) : 949 ~ 962
A. Moreno-Galindo / 2005 / A bilinear version of Holsztynski’s theorem on isometries of C(X)-spaces / Studia Mathematica 166 (1) : 83 ~ 91
B. A. Barnes / 2002 / Diameter preserving maps on various classes of function spaces / Studia Mathematica 153 (2) : 127 ~ 145
F. Cabello Sanchez / 1999 / Diameter preserving linear maps and isometries / Archiv der Mathematik (Basel) 73 (5) : 373 ~ 379
F. Gonzalez / 1999 / On homeomorphisms of groups of integer-valued functions / Extracta Mathematicae 14 (1) : 19 ~ 29
A. Moreno-Galindo / 2005 / A bilinear version of Holsztynski’s theorem on isometries of C(X)-spaces / Studia Mathematica 166 (1) : 83 ~ 91
B. A. Barnes / 2002 / Diameter preserving maps on various classes of function spaces / Studia Mathematica 153 (2) : 127 ~ 145
F. Cabello Sanchez / 1999 / Diameter preserving linear maps and isometries / Archiv der Mathematik (Basel) 73 (5) : 373 ~ 379
F. Gonzalez / 1999 / On homeomorphisms of groups of integer-valued functions / Extracta Mathematicae 14 (1) : 19 ~ 29
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