Geodesic
Symmetric properties of elementary operators
Novi Sad Journal of Mathematics, Tome 52 (2022) no. 1.

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We consider the elementary operator $M_{A,B}$, acting on the Hilbert-Schmidt class $C_{2}\left( {\mathcal{H}}\right) $, given by $M_{A,B}\left( T\right) =ATB$ with $A$ and $B$ bounded operators on ${\mathcal{H}}$. In this work, we establish necessary and sufficient conditions on $A$ and $B$ for $M_{A,B}$ to be a $2$-symmetric and $3$-symmetric. We also characterize binormality of elementary operators.
Publié le :
DOI : 10.30755/NSJOM.12475
Classification : 47A05, 47A55, 47B15
Keywords: Elementary operator, Symmetric operator, Binormal operator, Hilbert-Schmidt class 
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     title = {Symmetric properties of elementary operators},
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     year = {2022},
     doi = {10.30755/NSJOM.12475},
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Messaoud Guesba. Symmetric properties of elementary operators. Novi Sad Journal of Mathematics, Tome 52 (2022) no. 1. doi : 10.30755/NSJOM.12475. http://geodesic.mathdoc.fr/articles/10.30755/NSJOM.12475/

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