Geodesic
Coherent trace-class operators in Hilbert couples
Matematičeskie zametki, Tome 63 (1998) no. 6, pp. 866-872 
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/
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     author = {V. I. Ovchinnikov},
     title = {Coherent trace-class operators in {Hilbert} couples},
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     year = {1998},
     volume = {63},
     number = {6},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1998_63_6_a7/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

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.

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