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The weak-star closure of the unit ball in a hyperplane

Published online by Cambridge University Press:  20 January 2009

G. J. O. Jameson
G. J. O. Jameson
Affiliation:
University of Warwick, Coventry
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Let X be a normed linear space. We regard X as a subspace of its bidual X**. Polars will always be evaluated in the pair (X**, X*). We denote the closed unit ball in X by U, so that U0, U00 are the closed unit balls in X*, X** respectively. The weak topology induced by X on X* (the “weak-star” topology) will be denoted by σ(X), and cl() will denote σ(X)-closure.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 18 , Issue 1 , June 1972 , pp. 7 - 11
Copyright
Copyright © Edinburgh Mathematical Society 1972

References

REFERENCES

(1) Bourbaki, N., Espaces Vectoriels Topologiques, chap. III, IV, V (Paris, 1955).Google Scholar
(2) Day, M. M., Normed Linear Spaces (Berlin, 1962).CrossRefGoogle Scholar
(3) Jameson, G. J. O., The duality of pairs of wedges, Proc. London Math. Soc. (3) 24 (1972), 531–547.CrossRefGoogle Scholar
(4) Kerr, D. R., Seminorm-dual subspaces of the algebraic dual of a linear space, Math. Z. 104 (1968), 222–225.CrossRefGoogle Scholar