For cones in Hilbert spaces, regularity is equivalent to self-duality
Matematičeskie zametki, Tome 64 (1998) no. 4, pp. 616-621.

Voir la notice de l'article provenant de la source Math-Net.Ru

The theorem stating that a cone in a Hilbert space is regular if and only if it is self-dual is proved and applied to obtain new proofs of earlier results.
@article{MZM_1998_64_4_a14,
     author = {V. T. Khudalov},
     title = {For cones in {Hilbert} spaces, regularity is equivalent to self-duality},
     journal = {Matemati\v{c}eskie zametki},
     pages = {616--621},
     publisher = {mathdoc},
     volume = {64},
     number = {4},
     year = {1998},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1998_64_4_a14/}
}
TY  - JOUR
AU  - V. T. Khudalov
TI  - For cones in Hilbert spaces, regularity is equivalent to self-duality
JO  - Matematičeskie zametki
PY  - 1998
SP  - 616
EP  - 621
VL  - 64
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_1998_64_4_a14/
LA  - ru
ID  - MZM_1998_64_4_a14
ER  - 
%0 Journal Article
%A V. T. Khudalov
%T For cones in Hilbert spaces, regularity is equivalent to self-duality
%J Matematičeskie zametki
%D 1998
%P 616-621
%V 64
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_1998_64_4_a14/
%G ru
%F MZM_1998_64_4_a14
V. T. Khudalov. For cones in Hilbert spaces, regularity is equivalent to self-duality. Matematičeskie zametki, Tome 64 (1998) no. 4, pp. 616-621. http://geodesic.mathdoc.fr/item/MZM_1998_64_4_a14/

[1] Krein M. G., Rutman M. A., “Lineinye operatory, ostavlyayuschie invariantami konus v prostranstve Banakha”, UMN, 3:1 (1948), 3–95 | MR | Zbl

[2] Bratteli U., Robinson D., Operatornye algebry i kvantovaya statisticheskaya mekhanika, Mir, M., 1982 | Zbl

[3] Khudalov V. T., “Regulyarnye konusy v gilbertovom prostranstve”, Sib. matem. zh., 37:1 (1996), 193–196 | MR | Zbl

[4] Vlasov L. P., “Approksimativnye svoistva mnozhestv v lineinykh normirovannykh prostranstvakh”, UMN, 28:6 (1973), 3–66 | MR | Zbl

[5] Vulikh B. Z., Vvedenie v teoriyu konusov v normirovannykh prostranstvakh, Izd-vo Kalininskogo un-ta, Kalinin, 1977

[6] Vulikh B. Z., Spetsialnye voprosy geometrii konusov v normirovannykh prostranstvakh, Izd-vo Kalininskogo un-ta, Kalinin, 1978

[7] Moreau J.-J., “Décomposition orthogonale d'un espace hilbertien selon deux cônes mutuellement polaires”, C. R. Acad. Sci. Paris. Sér. I. Math., 225 (1962), 238–240 | MR

[8] Wittstock G., “Ordered normed tensor products”, Lecture Notes in Phys., 29, 1974, 67–84 | MR | Zbl