Characterizations of isometric isomorphisms between uniform algebras via nonlinear range-preserving properties

Hatori, Osamu; Miura, Takeshi; Takagi, Hiroyuki

doi:10.1090/S0002-9939-06-08500-5

Characterizations of isometric isomorphisms between uniform algebras via nonlinear range-preserving properties
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by Osamu Hatori, Takeshi Miura and Hiroyuki Takagi PDF

Proc. Amer. Math. Soc. 134 (2006), 2923-2930 Request permission

Abstract:

Let $T$ be a surjective mapping from a uniform algebra $A$ on a compact Hausdorff space $X$ onto a uniform algebra on a compact Hausdorff space $Y$. Suppose that $fg(X)=T(f)T(g)(Y)$ holds for every $f,g\in A$. Then we have that $T$ is an almost isometric isomorphism, which is a generalization of results of Molnár (2002) and Rao and Roy (2005).

References

Andrew Browder, Introduction to function algebras, W. A. Benjamin, Inc., New York-Amsterdam, 1969. MR 0246125
S. Kowalski and Z. Słodkowski, A characterization of multiplicative linear functionals in Banach algebras, Studia Math. 67 (1980), no. 3, 215–223. MR 592387, DOI 10.4064/sm-67-3-215-223
Lajos Molnár, Some characterizations of the automorphisms of $B(H)$ and $C(X)$, Proc. Amer. Math. Soc. 130 (2002), no. 1, 111–120. MR 1855627, DOI 10.1090/S0002-9939-01-06172-X
N. V. Rao and A. K. Roy, Multiplicatively spectrum-preserving maps of function algebras, Proc. Amer. Math. Soc. 133 (2005), no. 4, 1135–1142. MR 2117215, DOI 10.1090/S0002-9939-04-07615-4