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Subnormal operators with compact selfcommutator

Aleman, Alexandru LU (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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author
publishing date
type
Contribution to journal
publication status
published
subject
in
Manuscripta Mathematica
volume
91
issue
1
pages
353 - 367
publisher
Springer
external identifiers
  • scopus:0030292903
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
2009-09-16 13:10:02
date last changed
2017-01-01 04:35:15
@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},
  volume       = {91},
  year         = {1996},
}