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2 results

  • 18 - Dual Spaces of Banach Spaces

  • from Part IV - Banach Spaces
  • James C. Robinson, University of Warwick
  • Book:
    An Introduction to Functional Analysis
    Published online:
    21 March 2020
    Print publication:
    12 March 2020, pp 201-209

  • Summary

    We return to the topic of dual spaces. We prove Young’s inequality and Hölder’s inequality in the l^p and L^p spaces. We identify the dual spaces of l^p and L^p up to isometric isomorphisms: the proofs for l^p are presented in full, with the measure-theoretic proofs for L^p contained in Appendix B.

  • A SHARP VERSION OF BONSALL’S INEQUALITY

  • Part of
  • T. C. PEACHEY
  • Journal:
    Bulletin of the Australian Mathematical Society / Volume 92 / Issue 3 / December 2015
    Published online by Cambridge University Press:
    19 August 2015, pp. 397-404
    Print publication:
    December 2015
    • Article
      • You have access
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  • The best possible constant in a classical inequality due to Bonsall is established by relating that inequality to Young’s. Further, this extends the range of Bonsall’s inequality and yields a reverse inequality. It also provides a better constant in an inequality of Hardy, Littlewood and Pólya.