Hostname: page-component-cd9895bd7-lnqnp Total loading time: 0 Render date: 2024-12-26T07:06:02.290Z Has data issue: false hasContentIssue false

On copies of the null sequence Banach space in some vector measure spaces

Published online by Cambridge University Press:  17 April 2009

J.C. Ferrando
Affiliation:
Depto. Estadística y Matemática AplicadaUniversidad Miguel HernándezE-03202 Elche (Alicante), Spain e-mail: [email protected]
J.M. Amigó
Affiliation:
Depto. Estadística y Matemática AplicadaUniversidad Miguel HernándezE-03202 Elche (Alicante), Spain e-mail: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this note we extend a result of Drewnowski concerning copies of C0 in the Banach space of all countably additive vector measures and study some properties of complemented copies of C0 in several Banach spaces of vector measures.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1999

References

[1]Bessaga, C. and Pelczyński, A., ‘On bases and unconditional convergence of series in Banach spaces’, Studio. Math. 17 (1958), 151164.CrossRefGoogle Scholar
[2]Diestel, J., Sequences and series in Banach spaces, Graduate Texts in Math. 92 (Springer-Verlag, New York, Berlin, Heidelberg, Tokyo, 1984).Google Scholar
[3]Diestel, J. and Uhl, J., Vector measures, Math Surveys 15 (Amer. Math. Soc. Providence, R.I., 1977).CrossRefGoogle Scholar
[4]Drewnowski, L., ‘Copies of l∞ in an operator space’, Math. Proc. Camb. Phil. Soc. 108 (1990), 523526.CrossRefGoogle Scholar
[5]Drewnowski, L., ‘When does ca(σ, Y) contain a copy of l∞ or C 0?’, Proc. Amer. Math. Soc. 109 (1990), 747752.Google Scholar
[6]Ferrando, J.C., ‘When does bvcaX) contain a copy of l∞?’, Math. Scand. 74 (1994), 271274.CrossRefGoogle Scholar
[7]Ferrando, J.C., ‘Copies of C 0 in certain vector-valued function Banach spaces’, Math. Scand. 77 (1995), 148152.Google Scholar
[8]Ferrando, J.C. and Amigó, J.M., ‘On copies of C 0 in the bounded linear operator space’, submitted.Google Scholar
[9]Ferrando, J.C., Pellicer, M. López and Ruiz, L.M. Sánchez, Metrizable barrelled spaces, Pitman Research Notes in Math. 332 (Longman, Essex, 1995).Google Scholar
[10]Rosenthal, H.P., ‘On relatively disjoint families of measures, with some applications to Banach space theory’, Studia Math. 37 (1979), 1336.CrossRefGoogle Scholar