Geodesic
Coherent trace-class operators in Hilbert couples
Matematičeskie zametki, Tome 63 (1998) no. 6, pp. 866-872 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

In this paper it is proved that the ideal of trace-class operators acting in a couple of Hilbert spaces coincides with the ideal of coherent trace-class operators. A new formula is derived for the $K$-functional in the couple of algebras of all bounded linear operators acting in a Hilbert couple, and new interpolation theorems are proved for trace class operators. 
@article{MZM_1998_63_6_a7,
     author = {V. I. Ovchinnikov},
     title = {Coherent trace-class operators in {Hilbert} couples},
     journal = {Matemati\v{c}eskie zametki},
     pages = {866--872},
     year = {1998},
     volume = {63},
     number = {6},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1998_63_6_a7/}
}
TY  - JOUR
AU  - V. I. Ovchinnikov
TI  - Coherent trace-class operators in Hilbert couples
JO  - Matematičeskie zametki
PY  - 1998
SP  - 866
EP  - 872
VL  - 63
IS  - 6
UR  - http://geodesic.mathdoc.fr/item/MZM_1998_63_6_a7/
LA  - ru
ID  - MZM_1998_63_6_a7
ER  - 
%0 Journal Article
%A V. I. Ovchinnikov
%T Coherent trace-class operators in Hilbert couples
%J Matematičeskie zametki
%D 1998
%P 866-872
%V 63
%N 6
%U http://geodesic.mathdoc.fr/item/MZM_1998_63_6_a7/
%G ru
%F MZM_1998_63_6_a7
V. I. Ovchinnikov. Coherent trace-class operators in Hilbert couples. Matematičeskie zametki, Tome 63 (1998) no. 6, pp. 866-872. http://geodesic.mathdoc.fr/item/MZM_1998_63_6_a7/

[1] Ovchinnikov V. I., “The method of orbits in interpolation theory”, Math. Rep., 1:2 (1984), 349–515 | MR | Zbl

[2] Ovchinnikov V. I., “Interpolyatsiya operatorov klassov $S_p$ v gilbertovykh parakh”, Matem. zametki, 27:2 (1980), 273–282 | MR | Zbl

[3] Bergh J., Löfström J., Interpolation Spaces. An Introduction, Springer, Berlin–Heidelberg–New York, 1976 | Zbl

[4] Ovchinnikov V. I., “Vychislenie $K$-funktsionala dlya par prostranstv matrits”, Matem. zametki, 55:5 (1994), 98–109 | MR | Zbl

[5] Ovchinnikov V. I., “Interpolyatsiya v simmetrichno-normirovannykh idealakh operatorov, deistvuyuschikh v razlichnykh gilbertovykh prostranstvakh”, Funktsion. analiz i ego prilozh., 28:3 (1994), 80–82 | MR | Zbl

[6] Dmitriev V. I., Krein S. G., Ovchinnikov V. I., “Osnovy teorii interpolyatsii lineinykh operatorov”, Geometriya lineinykh prostranstv i teoriya operatorov, Yaroslavl, 1977, 31–74 | MR | Zbl