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

  • Part of
  • IRENE FERRANDO, ENRIQUE A. SÁNCHEZ PÉREZ
  • Journal:
    Journal of the Australian Mathematical Society / Volume 87 / Issue 2 / October 2009
    Published online by Cambridge University Press:
    09 October 2009, pp. 211-225
    Print publication:
    October 2009
    • Article
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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.