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ALMOST TRANSITIVITY IN $\mathcal{C}_0$ SPACES OF VECTOR-VALUED FUNCTIONS

Published online by Cambridge University Press:  15 September 2005

Antonio Aizpuru  and
Fernando Rambla
Antonio Aizpuru
Affiliation:
Departamento de Matemáticas, Facultad de Ciencias, Universidad de Cádiz, Campus del Río San Pedro s/n 11510, Puerto Real, Cádiz, Spain (antonio.aizpuru@uca.es; fernando.rambla@uca.es)
Fernando Rambla
Affiliation:
Departamento de Matemáticas, Facultad de Ciencias, Universidad de Cádiz, Campus del Río San Pedro s/n 11510, Puerto Real, Cádiz, Spain (antonio.aizpuru@uca.es; fernando.rambla@uca.es)
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Abstract

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By means of $M$-structure and dimension theory, we generalize some known results and obtain some new ones on almost transitivity in $\mathcal{C}_0(L,X)$. For instance, if $X$ has the strong Banach–Stone property, then almost transitivity of $\mathcal{C}_0(L,X)$ is divided into two weaker properties, one of them depending only on topological properties of $L$ and the other being closely related to the covering dimensions of $L$ and $X$. This leads to some non-trivial examples of almost transitive $\mathcal{C}_0(L,X)$ spaces.

Keywords

Primary 46B0446B2046E1557F45transitivityisometry$M$-structuredimension
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 48 , Issue 3 , October 2005 , pp. 513 - 529
Copyright
Copyright © Edinburgh Mathematical Society 2005