Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ \langle E,E'\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.


References [Enhancements On Off] (What's this?)

  • [1] P. L. Duren, B. W. Romberg and A. L. Shields, Linear functionals on $ {H^p}$ with $ 0 < p < 1$, J. Reine Angew. Math. 238 (1969), 32-60. MR 0259579 (41:4217)
  • [2] J. L. Kelley and I. Namioka, Linear topological spaces, The University Series in Higher Mathematics, Van Nostrand, Princeton, N. J., 1963. MR 29 #3851. MR 0166578 (29:3851)
  • [3] H. H. Schaefer, Topological vector spaces, Macmillan, New York, 1966. MR 33 #1689. MR 0193469 (33:1689)
  • [4] J. H. Shapiro, Extension of linear functionals on $ F$-spaces with bases, Duke Math. J. (to appear). MR 0270111 (42:5004)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 46.01

Retrieve articles in all journals with MSC: 46.01


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1970-0264361-X
Keywords: Hahn Banach Theorem, Mackey topology, weak topology, nonconvex topology
Article copyright: © Copyright 1970 American Mathematical Society

American Mathematical Society