Weak compactness in locally convex spaces
- 1 January 1968
- journal article
- research article
- Published by Cambridge University Press (CUP) in Glasgow Mathematical Journal
- Vol. 9 (2) , 123-127
- https://doi.org/10.1017/s0017089500000409
Abstract
In [2], R. C. James proved that a weakly closed subset X of a real Banach space is weakly compact if and only if each continuous linear form attains its supremum on X. He also extended the result to the locally convex case, and, in [5], J. D. Pryce gave a simplified proof of the general result that is recorded below for reference in the sequel.Keywords
This publication has 3 references indexed in Scilit:
- Weak Compactness in Locally Convex SpacesProceedings of the American Mathematical Society, 1966
- Weakly Compact SetsTransactions of the American Mathematical Society, 1964
- Shorter Notes: Weak Convergence of Bounded SequencesProceedings of the American Mathematical Society, 1963