Functions of compact operators under trace class perturbations
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866914679861805056 |
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| author | Aleksandrov, A. B. Peller, V. V. |
| author_facet | Aleksandrov, A. B. Peller, V. V. |
| contents | The paper studies the problem, for which continuous functions $f$ on the real line ${\Bbb R}$, the difference of the functions $f(B)-f(A)$ of self-adjoint operators $A$ and $B$ with trace class difference must also be of trace class. The main result of the paper shows that this happens if and only if the function $f$ is operator Lipschitz on a neighbourhood of zero. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_09843 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Functions of compact operators under trace class perturbations Aleksandrov, A. B. Peller, V. V. Functional Analysis Classical Analysis and ODEs Complex Variables Spectral Theory 47A55, 47B10 The paper studies the problem, for which continuous functions $f$ on the real line ${\Bbb R}$, the difference of the functions $f(B)-f(A)$ of self-adjoint operators $A$ and $B$ with trace class difference must also be of trace class. The main result of the paper shows that this happens if and only if the function $f$ is operator Lipschitz on a neighbourhood of zero. |
| title | Functions of compact operators under trace class perturbations |
| topic | Functional Analysis Classical Analysis and ODEs Complex Variables Spectral Theory 47A55, 47B10 |
| url | https://arxiv.org/abs/2402.09843 |