Subnormal operators with compact selfcommutator
(1996) In Manuscripta Mathematica 91(1). p.353367 Abstract
 If $S$ is a hyponormal operator, then Putnam's inequality gives an estimate on the norm of the selfcommutator $[S^*,S]$, while the BergerShaw 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 selfcommutator $[S^*,S]$, while the BergerShaw 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 operatorvalued 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)
Please use this url to cite or link to this publication:
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
 external identifiers

 scopus:0030292903
 ISSN
 14321785
 DOI
 10.1007/BF02567960
 language
 English
 LU publication?
 no
 id
 05ff96806f1b4205a714feb3a7f8d6a9 (old id 1467218)
 date added to LUP
 20090916 13:10:02
 date last changed
 20180529 10:02:11
@article{05ff96806f1b4205a714feb3a7f8d6a9, abstract = {If $S$ is a hyponormal operator, then Putnam's inequality gives an estimate on the norm of the selfcommutator $[S^*,S]$, while the BergerShaw 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 operatorvalued 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 = {14321785}, language = {eng}, number = {1}, pages = {353367}, publisher = {Springer}, series = {Manuscripta Mathematica}, title = {Subnormal operators with compact selfcommutator}, url = {http://dx.doi.org/10.1007/BF02567960}, volume = {91}, year = {1996}, }