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Transitivity of M-spaces and Wood's conjecture

Published online by Cambridge University Press:  01 November 1998

FÉLIX CABELLO SÁNCHEZ
FÉLIX CABELLO SÁNCHEZ
Affiliation:
Departamento de Matemáticas, Universidad de Extremadura 06071 Badajoz, Spain. e-mail: fcabello@unex.es
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Abstract

For a wide class of categories of Banach spaces, we show that the existence of an (almost) transitive element implies the existence of a separable almost transitive element. We give some applications to C0(L) spaces and abstract M-spaces. Next, we prove that Wood's conjecture on almost transitivity of the norm in C0(L) can be reduced to the case in which the one-point compactification of L is metrizable.

We construct a simple example of transitive M-space and we show the existence of almost transitive separable M-spaces that are isomorphic to C[0, 1]. These M-spaces have a rich M-structure and they are counterexamples for several questions about centralizers.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 124 , Issue 3 , November 1998 , pp. 513 - 520
Copyright
© Cambridge Philosophical Society 1998

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