UDK 517.982 OPERATOR IDEALS AND INTERPOLATION IN HILBERT COUPLES∗ V. I. Ovchinnikov (Voronezh State University) Поступила в редакцию 24.02.2014 г. <...> Abstract: this paper is a survey of results on the operator ideals, which are related to interpolation theory of linear operators. <...> We discuss the application of the real and complex method interpolation constructions to classical operator ideals, acting in scales of spaces, related to Hilbert couples, and some improvements of interpolation properties of linear operators, if these linear operators belong to some ideals. <...> INTERPOLATION THEOREMS FOR IDEALS MAPPING HILBERT COUPLES . . . . 149 5. <...> First, you are able to apply an interpolation construction to classical operator ideals and to obtain a new operator ideal. <...> If you obtain somewhat familiar ideal as a result, then you find a dependence between classical ideals, which can be useful. <...> And this phenomenon was historically the first, which was performed in the works of I.C.Gohberg and M.G.Krein (see [8]). <...> The second direction is to use somewhat complementary properties of operators from an ideal in order to get more sharp interpolation properties of these operators. <...> CLASSICAL IDEALS OF OPERATORS MAPPING HILBERT SPACES We shall suppose that readers are familiar with main fundamentals of the theory of cross-norm ideals of operators mapping Hilbert spaces. <...> In this Section we simply recall more or less common notations. <...> Let T be a bounded linear operator mapping a Hilbert space H into a Hilbert space F. This will be denoted by T : H →F and T ∈ L(H →F), where L(H →F) is the space of all bounded linear operators mapping H into F. Singular numbers or s-numbers of T ∈ L(H →F) are defined as follows sn(T) = inf K ∥T −K∥L(H→F), where infimum is taken over all K ∈ L(H → F) provided dim K(H) < n. <...> Hence we are able to construct a monotone positive ∥T∥L(H→F) and sn(T) ⩾ sn+1(T) for any n ∈ N. If the operator T is compact (which is denoted by T ∈ S∞(H → F)), then |T <...>