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The covering dimension of Wood spaces

Published online by Cambridge University Press:  25 July 2002

Félix Cabello Sánchez
Félix Cabello Sánchez
Affiliation:
Departamento de Matemáticas, Universidad de Extremadura, Avenida de Elvas, 06071-Badajoz, España e-mail: fcabello@unex.es
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Abstract

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A Banach space is called (almost) transitive if the isometry group acts (almost) transitively on the unit sphere. The main problems around transitivity are the Banach-Mazur conjecture that the only separable and transitive Banach spaces are the Hilbert ones (1930) and the Wood conjecture that C_0(L) cannot be almost transitive in its natural supremum norm unless L is a singleton (1982). In this note we give necessary and sufficient conditions on the locally compact space L for the (almost) transitivity of C_0(L). This will clarify the topological content of Wood's problem.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 44 , Issue 2 , May 2002 , pp. 311 - 316
Copyright
2002 Glasgow Mathematical Journal Trust