Banach Journal of Mathematical Analysis

Non-continuous linear functionals on topological vector spaces

Francisco J. Garcia-Pacheco

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Abstract

In this article we study the existence of non-continuous linear functionals on topological vector spaces. Both sufficient and necessary conditions for the existence of such maps are found.

Article information

Source
Banach J. Math. Anal., Volume 2, Number 1 (2008), 11 - 15.

Dates
First available in Project Euclid: 21 April 2009

Permanent link to this document
https://projecteuclid.org/euclid.bjma/1240336267

Digital Object Identifier
doi:10.15352/bjma/1240336267

Mathematical Reviews number (MathSciNet)
MR2378752

Zentralblatt MATH identifier
1134.46002

Subjects
Primary: 54C05: Continuous maps
Secondary: 46A03: General theory of locally convex spaces 46A55: Convex sets in topological linear spaces; Choquet theory [See also 52A07]

Keywords
convex balanced absorbing basis empty interior non-continuous linear functional

Citation

Garcia-Pacheco , Francisco J. Non-continuous linear functionals on topological vector spaces. Banach J. Math. Anal. 2 (2008), no. 1, 11 -- 15. doi:10.15352/bjma/1240336267. https://projecteuclid.org/euclid.bjma/1240336267


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References

  • R.E. Megginson, An Introduction to Banach Space Theory, Graduate Texts in Mathematics 183, New York, Springer-Verlag, 1998.
  • H.H. Schaefer, Topological Vector Spaces, Graduate Texts in Mathematics 3, New York, Springer-Verlag, 1999.