On commutators of square-zero Hilbert space operators
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913696546029568 |
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| author | Marcoux, Laurent W. Radjavi, Heydar Zhang, Yuanhang |
| author_facet | Marcoux, Laurent W. Radjavi, Heydar Zhang, Yuanhang |
| contents | Let $\mathcal{H}$ be a complex, separable Hilbert space, and set $\mathfrak{c}($NIL$_2)=\{ MN - NM : N, M \in \mathcal{B}(\mathcal{H}), M^2 = 0 = N^2 \}$. When $\dim\, \mathcal{H}$ is finite, we characterise the set $\mathfrak{c}($NIL$_2)$ and its norm-closure CLOS$(\mathfrak{c}($NIL$_2))$. In the infinite-dimensional setting, we characterise the intersection of CLOS$(\mathfrak{c}($NIL$_2))$ with the set of biquasitriangular operators, and we exhibit an index obstruction to belonging to CLOS$(\mathfrak{c}($NIL$_2))$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_15676 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On commutators of square-zero Hilbert space operators Marcoux, Laurent W. Radjavi, Heydar Zhang, Yuanhang Functional Analysis Primary: 47B47, Secondary: 47A58 Let $\mathcal{H}$ be a complex, separable Hilbert space, and set $\mathfrak{c}($NIL$_2)=\{ MN - NM : N, M \in \mathcal{B}(\mathcal{H}), M^2 = 0 = N^2 \}$. When $\dim\, \mathcal{H}$ is finite, we characterise the set $\mathfrak{c}($NIL$_2)$ and its norm-closure CLOS$(\mathfrak{c}($NIL$_2))$. In the infinite-dimensional setting, we characterise the intersection of CLOS$(\mathfrak{c}($NIL$_2))$ with the set of biquasitriangular operators, and we exhibit an index obstruction to belonging to CLOS$(\mathfrak{c}($NIL$_2))$. |
| title | On commutators of square-zero Hilbert space operators |
| topic | Functional Analysis Primary: 47B47, Secondary: 47A58 |
| url | https://arxiv.org/abs/2402.15676 |