Abstract
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 theK-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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Translated fromMatematicheskie Zametki, Vol. 63, No. 6, pp. 866–872, June, 1998.
This research was partially supported by the International Science Foundation and the Russian Government under grant JD 7100.
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Ovchinnikov, V.I. Coherent trace-class operators in Hilbert couples. Math Notes 63, 764–769 (1998). https://doi.org/10.1007/BF02312770
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DOI: https://doi.org/10.1007/BF02312770