Geodesic
Commutators on $L^2$-Spaces
Publications de l'Institut Mathématique, _N_S_97 (2015) no. 111, p. 125

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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 $N$.
DOI : 10.2298/PIM140205001K
Classification : 47A58 47B38
Keywords: commutators, Cauchy-type integrals 
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     author = {Vladimir Kapustin},
     title = {Commutators on $L^2${-Spaces}},
     journal = {Publications de l'Institut Math\'ematique},
     pages = {125 },
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     doi = {10.2298/PIM140205001K},
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     url = {http://geodesic.mathdoc.fr/articles/10.2298/PIM140205001K/}
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Vladimir Kapustin. Commutators on $L^2$-Spaces. Publications de l'Institut Mathématique, _N_S_97 (2015) no. 111, p. 125 . doi: 10.2298/PIM140205001K

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