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A concrete realization of the dual space of L1-spaces of certain vector and operator-valued measures

Part of: Linear function spaces and their duals Measures, integration, derivative, holomorphy Set functions, measures and integrals with values in abstract spaces

Published online by Cambridge University Press:  09 April 2009

Werner Ricker
Werner Ricker
Affiliation:
School of Mathematics and Physics Macquarie University North Ryde, NSW 2113, Australia
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Abstract

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For a given vector measure n, an important problem, but in practice a difficult one, is to give a concrete description of the dual space of L1(n). In this note such a description is presented for an important class of measures n, namely the spectral measures (in the sense of N. Dunford) and certain other vector and operator-valued measures that they naturally induce. The basic idea is to represent the L1-spaces of such measures as a more familiar space whose dual space is known.

MSC classification

Secondary: 28B05: Vector-valued set functions, measures and integrals 46G10: Vector-valued measures and integration 46E30: Spaces of measurable functions ($L^p$-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 42 , Issue 2 , April 1987 , pp. 265 - 279
Copyright
Copyright © Australian Mathematical Society 1987

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