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TENSOR PRODUCT REPRESENTATION OF THE (PRE)DUAL OF THE Lp-SPACE OF A VECTOR MEASURE

Part of: Measures, integration, derivative, holomorphy

Published online by Cambridge University Press:  09 October 2009

IRENE FERRANDO  and
ENRIQUE A. SÁNCHEZ PÉREZ
IRENE FERRANDO
Affiliation:
Instituto Universitario de Matemática Pura y Aplicada (IUMPA), Universidad Politécnica de Valencia, Camino de Vera, S/N, C.P. 46071, Valencia, Spain (email: irferpa@doctor.upv.es)
ENRIQUE A. SÁNCHEZ PÉREZ*
Affiliation:
Instituto Universitario de Matemática Pura y Aplicada (IUMPA), Universidad Politécnica de Valencia, Camino de Vera, S/N, C.P. 46071, Valencia, Spain (email: easancpe@mat.upv.es)
*
✉For correspondence; e-mail: easancpe@mat.upv.es
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Abstract

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The duality properties of the integration map associated with a vector measure m are used to obtain a representation of the (pre)dual space of the space Lp(m) of p-integrable functions (where 1<p<∞) with respect to the measure m. For this, we provide suitable topologies for the tensor product of the space of q-integrable functions with respect to m (where p and q are conjugate real numbers) and the dual of the Banach space where m takes its values. Our main result asserts that under the assumption of compactness of the unit ball with respect to a particular topology, the space Lp(m) can be written as the dual of a suitable normed space.

Keywords

vector measuresp-integrable functionstensor products

MSC classification

Secondary: 46G10: Vector-valued measures and integration
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 87 , Issue 2 , October 2009 , pp. 211 - 225
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2009

Footnotes

The first author acknowledges the support of the Instituto Universitario de Matemática Pura y Aplicada of the Universidad Politécnica de Valencia under grant FPI-UPV 2006–07. Research partially supported by Generalitat Valenciana (project GVPRE/2008/312), Universidad Politécnica (project PAID-06-09 Ref. 3093) and the Spanish Ministerio de Educación y Ciencia and FEDER, under project MTM2006-11690-C02-01.

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