Sequential and conditional compactness in the dual of a barrelled space

Ostling, Edward G.

doi:10.1090/S0002-9939-1974-0433178-9

Sequential and conditional compactness in the dual of a barrelled space
HTML articles powered by AMS MathViewer

by Edward G. Ostling

Proc. Amer. Math. Soc. 45 (1974), 123-124

DOI: https://doi.org/10.1090/S0002-9939-1974-0433178-9

PDF | Request permission

Abstract:

Let $E$ be a barrelled locally convex space and suppose ${T_{\mathcal {A}}}$ is a topology on the dual $E’$ of $E$ which is admissible for the duality $(E,E’)$. It is shown that each ${T_{\mathcal {A}}}$ sequentially compact subset of $E’$ is ${T_{\mathcal {A}}}$ conditionally compact.

References

Joe Howard, Mackey compactness in Banach spaces, Proc. Amer. Math. Soc. 37 (1973), 108–110. MR 312212, DOI 10.1090/S0002-9939-1973-0312212-X
J. L. Kelley and Isaac Namioka, Linear topological spaces, The University Series in Higher Mathematics, D. Van Nostrand Co., Inc., Princeton, N.J., 1963. With the collaboration of W. F. Donoghue, Jr., Kenneth R. Lucas, B. J. Pettis, Ebbe Thue Poulsen, G. Baley Price, Wendy Robertson, W. R. Scott, Kennan T. Smith. MR 0166578

Topologische linear Räume

24

40

A. P. Robertson and W. J. Robertson, Topological vector spaces, Cambridge Tracts in Mathematics and Mathematical Physics, No. 53, Cambridge University Press, New York, 1964. MR 0162118