Simple construction of spaces without the Hahn-Banach extension property

Jerzy Kąkol

Commentationes Mathematicae Universitatis Carolinae (1992)

  • Volume: 33, Issue: 4, page 623-624
  • ISSN: 0010-2628

Abstract

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An elementary construction for an abundance of vector topologies ξ on a fixed infinite dimensional vector space E such that ( E , ξ ) has not the Hahn-Banach extension property but the topological dual ( E , ξ ) ' separates points of E from zero is given.

How to cite

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Kąkol, Jerzy. "Simple construction of spaces without the Hahn-Banach extension property." Commentationes Mathematicae Universitatis Carolinae 33.4 (1992): 623-624. <http://eudml.org/doc/247361>.

@article{Kąkol1992,
abstract = {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 $(E,\xi )^\{\prime \}$ separates points of $E$ from zero is given.},
author = {Kąkol, Jerzy},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Hahn-Banach extension property; topological vector space; construction of spaces without the Hahn-Banach extension property; topological dual separates points; vector topologies},
language = {eng},
number = {4},
pages = {623-624},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Simple construction of spaces without the Hahn-Banach extension property},
url = {http://eudml.org/doc/247361},
volume = {33},
year = {1992},
}

TY - JOUR
AU - Kąkol, Jerzy
TI - Simple construction of spaces without the Hahn-Banach extension property
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1992
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 33
IS - 4
SP - 623
EP - 624
AB - 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 $(E,\xi )^{\prime }$ separates points of $E$ from zero is given.
LA - eng
KW - Hahn-Banach extension property; topological vector space; construction of spaces without the Hahn-Banach extension property; topological dual separates points; vector topologies
UR - http://eudml.org/doc/247361
ER -

References

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  1. Duren P.L., Romberg R.C., Shields A.L., Linear functionals in H p -spaces with 0 < p < 1 , J. Reine Angew. Math. 238 (1969), 32-60. (1969) MR0259579
  2. Kalton N.J., Basic sequences in F -spaces and their applications, Proc. Edinburgh Math. Soc. 19 (1974), 151-167. (1974) Zbl0296.46010MR0415259
  3. Kakol J., Nonlocally convex spaces and the Hahn-Banach extension property, Bull. Acad. Polon. Sci. 33 (1985), 381-393. (1985) Zbl0588.46004MR0821575
  4. Klee V., Exotic topologies for linear spaces, Proc. Symposium on General Topology and its Relations to Modern Algebra, Prague, 1961. Zbl0111.10701MR0154088
  5. Shapiro J.H., Examples of proper closed weakly dense subspaces in non-locally convex F -spaces, Israel J. Math. 7 (1969), 369-380. (1969) Zbl0202.39303MR0257696
  6. Wilansky A., Topics in Functional Analysis, Springer Verlag 45 (1967). Zbl0156.36103MR0223854

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