Article
| Title: | Perturbations of real parts of eigenvalues of bounded linear operators in a Hilbert space (English) |
| Author: | Gil', Michael |
| Language: | English |
| Journal: | Czechoslovak Mathematical Journal |
| ISSN: | 0011-4642 (print) |
| ISSN: | 1572-9141 (online) |
| Volume: | 74 |
| Issue: | 2 |
| Year: | 2024 |
| Pages: | 567-573 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | 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. (English) |
| Keyword: | Hilbert space |
| Keyword: | linear operator |
| Keyword: | eigenvalue |
| Keyword: | Kato theorem |
| Keyword: | Weyl inequality |
| MSC: | 47A10 |
| MSC: | 47A55 |
| MSC: | 47B10 |
| DOI: | 10.21136/CMJ.2024.0468-23 |
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| Date available: | 2024-07-10T14:56:55Z |
| Last updated: | 2024-07-15 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/152458 |
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