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On Convergence of Projections in Locally Convex Spaces

Published online by Cambridge University Press:  20 November 2018

J. E. Simpson
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This note is concerned with the extension to locally convex spaces of a theorem of J. Y. Barry [ 1 ]. The basic assumptions are as follows. E is a separated locally convex topological vector space, henceforth assumed to be barreled. E' is its strong dual. For any subset A of E, we denote by w(A) the closure of A in the σ-(E, E')-topology. See [ 2 ] for further information about locally convex spaces. By a projection we shall mean a continuous linear mapping of E into itself which is idempotent.

Type
Notes and Problems
Information
Canadian Mathematical Bulletin , Volume 9 , Issue 1 , April 1966 , pp. 107 - 110
Copyright
Copyright © Canadian Mathematical Society 1966

References

1. Barry, J. Y., On the convergence of ordered sets of projections, Proc. Amer. Math. Soc., 5 (1954), 313-314.Google Scholar
2. Bourbaki, N., Espaces Vectoriels Topologiques. Paris, 1953-1955.Google Scholar
3. Dunford, N. and Schwartz, J., Linear Operators. New York, 1958.Google Scholar