Extensions of convex functionals on convex cones

E. Ignaczak; A. Paszkiewicz

Applicationes Mathematicae (1998)

  • Volume: 25, Issue: 3, page 381-386
  • ISSN: 1233-7234

Abstract

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We prove that under some topological assumptions (e.g. if M has nonempty interior in X), a convex cone M in a linear topological space X is a linear subspace if and only if each convex functional on M has a convex extension on the whole space X.

How to cite

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Ignaczak, E., and Paszkiewicz, A.. "Extensions of convex functionals on convex cones." Applicationes Mathematicae 25.3 (1998): 381-386. <http://eudml.org/doc/219211>.

@article{Ignaczak1998,
abstract = {We prove that under some topological assumptions (e.g. if M has nonempty interior in X), a convex cone M in a linear topological space X is a linear subspace if and only if each convex functional on M has a convex extension on the whole space X.},
author = {Ignaczak, E., Paszkiewicz, A.},
journal = {Applicationes Mathematicae},
keywords = {Hilbert space; convex functional; convex cone; linear topological space; convex extension},
language = {eng},
number = {3},
pages = {381-386},
title = {Extensions of convex functionals on convex cones},
url = {http://eudml.org/doc/219211},
volume = {25},
year = {1998},
}

TY - JOUR
AU - Ignaczak, E.
AU - Paszkiewicz, A.
TI - Extensions of convex functionals on convex cones
JO - Applicationes Mathematicae
PY - 1998
VL - 25
IS - 3
SP - 381
EP - 386
AB - We prove that under some topological assumptions (e.g. if M has nonempty interior in X), a convex cone M in a linear topological space X is a linear subspace if and only if each convex functional on M has a convex extension on the whole space X.
LA - eng
KW - Hilbert space; convex functional; convex cone; linear topological space; convex extension
UR - http://eudml.org/doc/219211
ER -

References

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  1. [1] J. M. Harrison and D. M. Kreps, Martingales and arbitrage in multiperiod securities markets, J. Econom. Theory 20 (1979), 381-408. Zbl0431.90019
  2. [2] R. B. Holmes, Geometric Functional Analysis and its Applications, Springer, Berlin, 1975. Zbl0336.46001
  3. [3] E. Jouini, Market imperfections, equilibrium and arbitrage, in: Financial Mathematics, Lecture Notes in Math. 1656, Springer, Berlin, 1997, 247-307. Zbl0910.90010
  4. [4] M. Musiela and M. Rutkowski, Martingale Methods in Financial Modeling, Springer, Berlin, 1997. Zbl0906.60001
  5. [5] S. Rolewicz, Functional Analysis and Control Theory, PWN-Polish Sci. Publ., Warszawa, 1971. 

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