On simultaneous approximation of several eigenvalues of a semi-definite self-adjoint linear operator in a Hilbert space

A lower semi-definite self-adjoint linear operator in a Hilbert space is taken whose discrete spectrum is not empty and comprises at least several eigenvalues ${\lambda }_{min}={\lambda }_1⩽\dots ⩽{\lambda }_m<{\sigma }_{ess}$. The problem of approximation of these eigenvalues by eigenvalues of some linear operator in a finite-dimensional space of the dimension $s$ is considered and solved. The accuracy of the approximation obtained becomes unlimitedly high as $s\to \mathrm{\infty }$.