# Extensions of convex functionals on convex cones

Applicationes Mathematicae (1998)

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

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topIgnaczak, 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

top- [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] R. B. Holmes, Geometric Functional Analysis and its Applications, Springer, Berlin, 1975. Zbl0336.46001
- [3] E. Jouini, Market imperfections, equilibrium and arbitrage, in: Financial Mathematics, Lecture Notes in Math. 1656, Springer, Berlin, 1997, 247-307. Zbl0910.90010
- [4] M. Musiela and M. Rutkowski, Martingale Methods in Financial Modeling, Springer, Berlin, 1997. Zbl0906.60001
- [5] S. Rolewicz, Functional Analysis and Control Theory, PWN-Polish Sci. Publ., Warszawa, 1971.

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