A matrix modification of formulas for the Hermite interpolation of operators in a Hilbert space

Necessary and sufficient conditions for the existence of an Hermite operator polynomial in a Hilbert space are obtained, and Hermite interpolating operator formulas containing vectors and matrices of lower (in comparison with E. G. Kashpur, V. L. Makarov, and V. V. Khlobystov, “On the problem of Hermite interpolation of operators in a Hilbert space”, Vychisl. Prikl. Mat., No. 78, 38–48 (1994)) dimension are derived. Translated fromObchyslyuval'na ta Prykladna Matematyka, No. 78, 1994, pp. 28–37.