1 results
On commutators of square-zero Hilbert space operators
- Part of
-
- Journal:
- Canadian Journal of Mathematics , First View
- Published online by Cambridge University Press:
- 17 February 2025, pp. 1-36
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- Article
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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 
.
. When 
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 
.