Subnormal operators with compact selfcommutator
(1996) In Manuscripta Mathematica 91(1). p.353-367- Abstract
- 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.
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.
The author also proves some trace estimates for commutators.... (More) - 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.
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.
The author also proves some trace estimates for commutators. His basic method is a careful analysis of positive operator-valued measures.
Abstract For an arbitrary subnormal operator we estimate the essential norm and trace of commutators of the form [T u, S], whereT u is a Toeplitz operator with continuous symbol. In particular, we obtain criteria for the compactness of [S *,S]. The trace estimates apply to multiplication operators on Hardy spaces over general domains. (Less)
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http://lup.lub.lu.se/record/1467218
- author
- Aleman, Alexandru ^{LU}
- publishing date
- 1996
- type
- Contribution to journal
- publication status
- published
- subject
- in
- Manuscripta Mathematica
- volume
- 91
- issue
- 1
- pages
- 353 - 367
- publisher
- Springer
- ISSN
- 1432-1785
- DOI
- 10.1007/BF02567960
- language
- English
- LU publication?
- no
- id
- 05ff9680-6f1b-4205-a714-feb3a7f8d6a9 (old id 1467218)
- date added to LUP
- 2016-04-01 11:50:06
- date last changed
- 2020-05-04 04:29:25
@article{05ff9680-6f1b-4205-a714-feb3a7f8d6a9, abstract = {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> <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> <br/><br> The author also proves some trace estimates for commutators. His basic method is a careful analysis of positive operator-valued measures.<br/><br> <br/><br> Abstract For an arbitrary subnormal operator we estimate the essential norm and trace of commutators of the form [T u, S], whereT u is a Toeplitz operator with continuous symbol. In particular, we obtain criteria for the compactness of [S *,S]. The trace estimates apply to multiplication operators on Hardy spaces over general domains.}, author = {Aleman, Alexandru}, issn = {1432-1785}, language = {eng}, number = {1}, pages = {353--367}, publisher = {Springer}, series = {Manuscripta Mathematica}, title = {Subnormal operators with compact selfcommutator}, url = {http://dx.doi.org/10.1007/BF02567960}, doi = {10.1007/BF02567960}, volume = {91}, year = {1996}, }