Nonconvex linear topologies with the Hahn Banach extension property.
Authors:
D. A. Gregory and J. H. Shapiro
Journal:
Proc. Amer. Math. Soc. 25 (1970), 902-905
MSC:
Primary 46.01
DOI:
https://doi.org/10.1090/S0002-9939-1970-0264361-X
MathSciNet review:
0264361
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Abstract | References | Similar Articles | Additional Information
Abstract: Let $\langle E,Eā\rangle$ be a dual pair of vector spaces. It is shown that whenever the weak and Mackey topologies on $E$ are different there is a nonconvex linear topology between them. In particular this provides a large class of nonconvex linear topologies having the Hahn Banach Extension Property.
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- 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
- Helmut H. Schaefer, Topological vector spaces, The Macmillan Co., New York; Collier-Macmillan Ltd., London, 1966. MR 0193469
- Joel H. Shapiro, Extension of linear functionals on $F$-spaces with bases, Duke Math. J. 37 (1970), 639ā645. MR 270111
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Additional Information
Keywords:
Hahn Banach Theorem,
Mackey topology,
weak topology,
nonconvex topology
Article copyright:
© Copyright 1970
American Mathematical Society