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On commutators of square-zero Hilbert space operators
Published online by Cambridge University Press: 17 February 2025
Abstract
Let $\mathcal H$ be a complex, separable Hilbert space, and set
. When
$\dim \, \mathcal H$ is finite, we characterise the set
and its norm-closure
. In the infinite-dimensional setting, we characterise the intersection of
with the set of biquasitriangular operators, and we exhibit an index obstruction to belonging to
.
MSC classification
- Type
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- Information
- Copyright
- © The Author(s), 2025. Published by Cambridge University Press on behalf of Canadian Mathematical Society
Footnotes
Laurent W. Marcoux is supported in part by NSERC (Canada); Yuanhang Zhang is supported in part by National Natural Science Foundation of China (No.: 12071174)
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