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Duality

  • Michel Willem
Chapter
Part of the Cornerstones book series (COR)

Abstract

The dual X of a normed space X is the space of continuous linear functionals on X. We define the weak convergence in X in Sect.5.1. We characterize X when X is a uniformly convex smooth Banach space (Sect.5.2), a Hilbert space (Sect.5.3), and a Lebesgue space (Sect.5.4).

References

  1. 35.
    James, R.C.: Orthogonality and linear functionals in normed linear spaces. Trans. Am. Math. Soc. 61, 265–292 (1947)CrossRefGoogle Scholar
  2. 61.
    Riesz, F.: Sur les opérations fonctionnelles linéaires. C. R. Acad. Sci. Paris 149, 974–977 (1909)Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2013

Authors and Affiliations

  • Michel Willem
    • 1
    • 2
  1. 1.Université catholique de LouvainLouvain-la-NeuveBelgium
  2. 2.Académie royale de BelgiqueBrusselsBelgium

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