Simple construction of spaces without the Hahn-Banach extension property
Kąkol, Jerzy
Commentationes Mathematicae Universitatis Carolinae, Tome 33 (1992), p. 623-624 / Harvested from Czech Digital Mathematics Library
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An elementary construction for an abundance of vector topologies $\xi $ on a fixed infinite dimensional vector space $E$ such that $(E,\xi )$ has not the Hahn-Banach extension property but the topological dual $(E,\xi )'$ separates points of $E$ from zero is given.

Publié le : 1992-01-01
Classification:  46A22 
@article{118533,
     author = {Jerzy K\k akol},
     title = {Simple construction of spaces without the Hahn-Banach extension property},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {33},
     year = {1992},
     pages = {623-624},
     zbl = {0777.46003},
     mrnumber = {1240183},
     language = {en},
     url = {http://dml.mathdoc.fr/item/118533}
}

Kąkol, Jerzy. Simple construction of spaces without the Hahn-Banach extension property. Commentationes Mathematicae Universitatis Carolinae, Tome 33 (1992) pp. 623-624. http://gdmltest.u-ga.fr/item/118533/

Duren P.L.; Romberg R.C.; Shields A.L. Linear functionals in $H^p$-spaces with $0, J. Reine Angew. Math. 238 (1969), 32-60. (1969) | MR 0259579

Kalton N.J. Basic sequences in $F$-spaces and their applications, Proc. Edinburgh Math. Soc. 19 (1974), 151-167. (1974) | MR 0415259 | Zbl 0296.46010

Kakol J. Nonlocally convex spaces and the Hahn-Banach extension property, Bull. Acad. Polon. Sci. 33 (1985), 381-393. (1985) | MR 0821575 | Zbl 0588.46004

Klee V. Exotic topologies for linear spaces, Proc. Symposium on General Topology and its Relations to Modern Algebra, Prague, 1961. | MR 0154088 | Zbl 0111.10701

Shapiro J.H. Examples of proper closed weakly dense subspaces in non-locally convex $F$-spaces, Israel J. Math. 7 (1969), 369-380. (1969) | MR 0257696 | Zbl 0202.39303

Wilansky A. Topics in Functional Analysis, Springer Verlag 45 (1967). | MR 0223854 | Zbl 0156.36103