| Title | Subnormal operators with compact selfcommutator |
| Authors | Alexandru Aleman |
| Alternative Location | http://dx.doi.org/10.1007/B..., Restricted Access |
| Publication | manuscripta mathematica |
| Year | 1996 |
| Volume | 91 |
| Issue | 1 |
| Pages | 353 - 367 |
| Document type | Article |
| Status | Published |
| Quality controlled | Yes |
| Language | eng |
| Publisher | Springer Berlin / Heidelberg |
| Abstract English | If $S$ is a hyponormal operator, then Putnam's inequality gives an estimate on the norm of the self-commutator $S^*,S$, while the Berger-Shaw theorem gives (under appropriate cyclicity hypotheses) a corresponding estimate on the trace of $S^*,S$. Of course these results hold when $S$ is subnormal. <br> <br> In the subnormal setting, the author obtains useful estimates on the norm and essential norm of commutators of the form\break $T_u,S$, where $T_u$ is a Toeplitz operator with continuous symbol $u$. A consequence is the following compactness condition. If the essential spectrum of $S$ is the boundary of an open set, then $S^*,S$ is compact. <br> <br> The author also proves some trace estimates for commutators. His basic method is a careful analysis of positive operator-valued measures. |
| ISBN/ISSN/Other | ISSN: 1432-1785 (Online) |
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