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Ultrabornological Bochner integrable function spaces
Published online by Cambridge University Press: 17 April 2009
Abstract
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If (Ω, Σ, μ) is a finite measure space and X is a normed space such that X* has the Radon-Nikodym property with respect to μ, we show first that each space Lp(μ, x), 1 < p < ∞, is ultrabornological whenever μ is atomless. When μ is arbitrary, we prove later on that the space Lp(μ, X) is ultrabornological if X* has the Radon-Nikodym property with respect to μ and X is itself an ultrabornological space.
- Type
- Research Article
- Information
- Bulletin of the Australian Mathematical Society , Volume 47 , Issue 1 , February 1993 , pp. 119 - 126
- Copyright
- Copyright © Australian Mathematical Society 1993
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