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A lower semi-definite self-adjoint linear operator in a Hilbert space istaken whose discrete spectrum is not empty and comprises at least severaleigenvalues$\lambda_{min}=\lambda_1\leqslant\ldots\leqslant\lambda_m<\sigma_{ess}$. Theproblem of approximation of these eigenvalues by eigenvalues of some linearoperator in a finite-dimensional space of the dimension $s$ is considered andsolved. The accuracy of the approximation obtained becomes unlimitedly high as$s\to\infty$.

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