ABOUT ONE "SMALL" ALGEBRA OF OPERATORS ACTING IN THE WEIGHT SPACES

The paper describes a special case of a family of Hilbert spaces. The operators that map these spaces into themselves have a simple representation in the form of the sum of a scalar operator and the operator which belong to some operator ideal. Earlier, V.I. Ovchinnikov hypothesized that the structure of operators operating in interpolation families is related to the "number" of interpolation spaces. The example given in the paper confirms this hypothesis.