Eigenvalue collision and exotic preservers on semisimple operators
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866911576219451392 |
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| author | Chirvasitu, Alexandru |
| author_facet | Chirvasitu, Alexandru |
| contents | We classify $n\times n$-matrix-valued continuous commutativity and spectrum preservers defined on spaces of (a) normal, (b) semisimple and (c) arbitrary $n\times n$ matrices with spectra contained in sufficiently connected subsets $\mathcal{X}\subseteq \mathbb{C}$, generalizing a number of results due to Šemrl, Gogić, Tomašević and the author among others. In case (a) these are always conjugations or transpose conjugations, while in cases (b) and (c) qualitatively distinct possibilities arise depending on the local regularity of the complex-conjugation map close to coincident-eigenvalue loci of $\mathcal{X}^n$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_07062 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Eigenvalue collision and exotic preservers on semisimple operators Chirvasitu, Alexandru Spectral Theory Combinatorics Functional Analysis General Topology 15A86, 47B49, 47B15, 54D05, 47A10, 51A05, 39A70, 47B39 We classify $n\times n$-matrix-valued continuous commutativity and spectrum preservers defined on spaces of (a) normal, (b) semisimple and (c) arbitrary $n\times n$ matrices with spectra contained in sufficiently connected subsets $\mathcal{X}\subseteq \mathbb{C}$, generalizing a number of results due to Šemrl, Gogić, Tomašević and the author among others. In case (a) these are always conjugations or transpose conjugations, while in cases (b) and (c) qualitatively distinct possibilities arise depending on the local regularity of the complex-conjugation map close to coincident-eigenvalue loci of $\mathcal{X}^n$. |
| title | Eigenvalue collision and exotic preservers on semisimple operators |
| topic | Spectral Theory Combinatorics Functional Analysis General Topology 15A86, 47B49, 47B15, 54D05, 47A10, 51A05, 39A70, 47B39 |
| url | https://arxiv.org/abs/2604.07062 |