대한수학회보 (Bulletin of the Korean Mathematical Society)
- 제32권1호
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- Pages.85-91
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- 1995
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- 1015-8634(pISSN)
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- 2234-3016(eISSN)
ISOMETRIES WITH SMALL BOUND ON $C^1$ (X) SPACES
- Jun, Kil-Woung (Department of Mathematics, Chungnam National University, Taejon 305-764) ;
- Lee, Yang-Hi (Department of Mathematics Education, Kong Ju National Teachers College, Kong Ju 314-060)
- 발행 : 1995.02.01
초록
For a locally compact Hausdorff space, we denote by $C_0(X)$ the Banach space of all continuous complex valued functions defined on X which vanish at infinity, equipped with the usual sup norm. In case X is compact, we write C(X) instead of $C_0(X)$. A well-known Banach-Stone theorem states that the existence of an isometry between the function spaces $C_0(X)$ and $C_0(Y)$ implies X and Y are homemorphic. D. Amir [1] and M. Cambern [2] independently generalized this theorem by proving that if $C_0(X)$ and $C_0(Y)$ are isomorphic under an isomorphism T satisfying $\left\
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