The uniform boundedness principle for arbitrary locally convex spaces
DOI:
https://doi.org/10.4067/S0716-09172007000300002Abstract
We establish uniform boundedness principle for pointwise bounded families of continuous linear operators between locally convex spaces which require no assumptions such as barrelledness on the domain space of the operators. We give applications of the result to separately continuous bilinear operators between locally convex spaces.
References
[B] Bourbaki, N., Topological Vector Spaces, Springer-Verlag, Berlin, (1987).
[K] Köthe, G., Topological Vector Spaces I, Springer-Verlag, Berlin, (1983).
[K2] Köthe, G, Topological Vector Spaces II, Springer-Verlag, Berlin, (1979).
[LC] Li, R. and Cho, M., A Banach-Steinhaus Type Theorem Which is Valid for every Locally Convex Space, Applied Functional Anal., 1, pp. 146-147, (1993).
[S] Swartz, C., An Introduction to Functional Analysis, Marcel Dekker, N. Y., (1992).
[W] Wilansky, A., Modern Methods in Topological Vector Spaces, McGraw Hill, N. Y., (1978).
[K] Köthe, G., Topological Vector Spaces I, Springer-Verlag, Berlin, (1983).
[K2] Köthe, G, Topological Vector Spaces II, Springer-Verlag, Berlin, (1979).
[LC] Li, R. and Cho, M., A Banach-Steinhaus Type Theorem Which is Valid for every Locally Convex Space, Applied Functional Anal., 1, pp. 146-147, (1993).
[S] Swartz, C., An Introduction to Functional Analysis, Marcel Dekker, N. Y., (1992).
[W] Wilansky, A., Modern Methods in Topological Vector Spaces, McGraw Hill, N. Y., (1978).
Published
2017-04-12
How to Cite
[1]
C. Swartz, “The uniform boundedness principle for arbitrary locally convex spaces”, Proyecciones (Antofagasta, On line), vol. 26, no. 3, pp. 245-251, Apr. 2017.
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