Abstract

We investigate suitable equivalence relations on locally convex cones which give rise to the definition of a locally convex quotient cone. In the special case of a locally convex vector space, this reduces to the known concept of quotient spaces. We recover most aspects of this case for our more general setting and provide a range of examples and applications for this approach, most of them new.

Author information

Contact details are reproduced from the original publication and may be historical.

Walter Roth

Dept. of Mathematics, Universiti Brunei Darussalam, Gadong BE1410, Brunei Darussalam

walter.roth@ubd.edu.bn

Keywords

  • Locally convex cones
  • equivalence relations
  • quotients

Mathematics Subject Classification

46A40, 46A03, 46A20

References

  1. B. Fuchssteiner, W. Lusky: Convex Cones, North Holland Math. Studies 56, North-Holland, Amsterdam (1981).Google Scholar
  2. L. V. Kantorovič: Functional Analysis in Partially Ordered Spaces, Gostekhizdat, Moscow (1950) (in Russian).Google Scholar
  3. K. Keimel, W. Roth: Ordered Cones and Approximation, Lecture Notes in Mathematics 1517, Springer, Berlin (1992).https://doi.org/10.1007/BFb0089190Google Scholar
  4. W. Roth: Operator-Valued Measures and Integrals for Cone-Valued Functions, Lecture Notes in Mathematics 1964, Springer, Berlin (2009).Google Scholar
  5. W. Roth: Hahn-Banach type theorems for locally convex cones, J. Aust. Math. Soc., Ser. A 68(1) (2000) 104–125.https://doi.org/10.1017/S1446788700001609Google Scholar
  6. W. Roth: Separation properties for locally convex cones, J. Convex Analysis 9(1) (2002) 301–307.https://doi.org/10.68381/jca09018Google Scholar
  7. W. Roth: Boundedness and connectedness components for locally convex cones, N. Z. J. Math. 34 (2005) 143–158.Google Scholar
  8. H. H. Schäfer: Topological Vector Spaces, Springer, New York (1980).Google Scholar
  9. S. Willard: General Topology, Addison-Wesley, Reading (1970).Google Scholar

Suggested citation

W. Roth. “Locally Convex Quotient Cones.” Journal of Convex Analysis 18 (2011), No. 4, 903–913. https://doi.org/10.68381/jca18057

Download BibTeXPublished by Heldermann Verlag.

Published by Heldermann Verlag, 2011. Rights now held by Banach Press LLC.