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Sectional representation of Banach modules and their multipliers

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  • Terje Hõim
  • D. A. Robbins

Abstract

Let X be a Banach module over the commutative Banach algebra A with maximal ideal space Δ . We show that there is a norm-decreasing representation of X as a space of bounded sections in a Banach bundle π : ℰ → Δ , whose fibers are quotient modules of X . There is also a representation of M ( X ) , the space of multipliers T : A → X , as a space of sections in the same bundle, but this representation may not be continuous. These sectional representations subsume results of various authors over the past three decades.

Suggested Citation

  • Terje Hõim & D. A. Robbins, 2003. "Sectional representation of Banach modules and their multipliers," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2003, pages 1-9, January.
    • Handle: RePEc:hin:jijmms:493921
    DOI: 10.1155/S0161171203207109
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