Perturbations of operators and non-commutative condensers, an update on the quasicentral modulus
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908289931935744 |
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| author | Voiculescu, Dan-Virgil |
| author_facet | Voiculescu, Dan-Virgil |
| contents | This is an update on the quasicentral modulus, an invariant for an n-tuple of Hilbert space operators and a rearrangement invariant norm, that plays a key-role in sharp multivariable generalizations of the classical Weyl-von Neumann-Kuroda and Kato-Rosenblum theorems of perturbation theory. There are also connections with self-similar measures on certain fractals and to the Kolmogorov-Sinai dynamical entropy. Some open problems are also pointed out. Recently a non-commutative analogy with condenser capacity in nonlinear potential theory is emerging, that provides a new perspective on the subject. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2503_23248 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Perturbations of operators and non-commutative condensers, an update on the quasicentral modulus Voiculescu, Dan-Virgil Functional Analysis Spectral Theory Primary: 47L20, Secondary: 31C45, 46L89 This is an update on the quasicentral modulus, an invariant for an n-tuple of Hilbert space operators and a rearrangement invariant norm, that plays a key-role in sharp multivariable generalizations of the classical Weyl-von Neumann-Kuroda and Kato-Rosenblum theorems of perturbation theory. There are also connections with self-similar measures on certain fractals and to the Kolmogorov-Sinai dynamical entropy. Some open problems are also pointed out. Recently a non-commutative analogy with condenser capacity in nonlinear potential theory is emerging, that provides a new perspective on the subject. |
| title | Perturbations of operators and non-commutative condensers, an update on the quasicentral modulus |
| topic | Functional Analysis Spectral Theory Primary: 47L20, Secondary: 31C45, 46L89 |
| url | https://arxiv.org/abs/2503.23248 |