EMIS ELibM Electronic Journals Publications de l'Institut Mathématique, Nouvelle Série
Vol. 97(111), pp. 125–137 (2015)

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COMMUTATORS ON $L^2$-SPACES

Vladimir Kapustin

St. Petersburg Department of the Steklov Mathematical Institute, St. Petersburg, Russia

Abstract: Given a normal operator $N$ on a Hilbert space and an operator $X$ for which the commutator $K=XN-NX$ belongs to the Hilbert–Schmidt class, we discuss the possibility to represent $X$ as a sum of a Cauchy transform corresponding to $K$ in the spectral representation of $N$ and an operator commuting with $N$.

Keywords: commutators, Cauchy-type integrals

Classification (MSC2000): 47A58; 47B38

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Electronic fulltext finalized on: 16 Apr 2015. This page was last modified: 21 Apr 2015.

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