| Abstrakt: |
Abstract: Let $A$ be a bounded linear operator in a complex separable Hilbert space $\mathcal{H}$, and $S$ be a selfadjoint operator in $\mathcal{H}$. Assuming that $A-S$ belongs to the Schatten-von Neumann ideal $\mathcal{S}_p$ $(p> 1),$ we derive a bound for $\sum_k| {\rm R} \lambda_k(A)-\lambda_k(S)|^p$, where $\lambda_k(A)$ $(k=1, 2, \dots)$ are the eigenvalues of $A$. Our results are formulated in terms of the "extended" eigenvalue sets in the sense introduced by T. Kato. In addition, in the case $p=2$ we refine the Weyl inequality between the real parts of the eigenvalues of $A$ and the eigenvalues of its Hermitian component. |
