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ON A CONJECTURE OF WOOD

Published online by Cambridge University Press:  31 January 2005

KAZUHIRO KAWAMURA
KAZUHIRO KAWAMURA
Affiliation:
Institute of Mathematics, University of Tsukuba, Tsukuba, Ibaraki 305-8071, Japan e-mail: kawamura@math.tsukuba.ac.jp
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Abstract

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We show that there exists a locally compact separable metrizable space $L$ such that $C_{0}(L)$, the Banach space of all continuous complex-valued functions vanishing at infinity with the supremum norm, is almost transitive. Due to a result of Greim and Rajagopalan [3], this implies the existence of a locally compact Hausdorff space $\tilde L$ such that $C_{0}(\tilde L)$ is transitive, disproving a conjecture of Wood [9]. We totally owe our construction to a topological characterization due to Sánches [8].

Keywords

54C3546B0454G99
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 47 , Issue 1 , January 2005 , pp. 1 - 5
Copyright
2005 Glasgow Mathematical Journal Trust