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Transitivity in spaces of vector-valued functions

Part of: Linear function spaces and their duals Normed linear spaces and Banach spaces; Banach lattices

Published online by Cambridge University Press:  05 August 2010

Félix Cabello Sánchez
Félix Cabello Sánchez
Affiliation:
Departamento de Matemáticas, Universidad de Extremadura, 06071 Badajoz, Spain (fcabello@unex.es)
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Abstract

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We exhibit a real Banach space M such that C(K,M) is almost transitive if K is the Cantor set, the growth of the integers in its Stone–Čech compactification or the maximal ideal space of L∞. For finite K, the space C(K,M) = M|K| is even transitive.

Keywords

Banach spaceisometrytransitivityvector-valued function

MSC classification

Secondary: 46B04: Isometric theory of Banach spaces 46E40: Spaces of vector- and operator-valued functions
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 53 , Issue 3 , October 2010 , pp. 601 - 608
Copyright
Copyright © Edinburgh Mathematical Society 2010

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