Geodesic
Product equivalence of quasihomogeneous Toeplitz operators on the harmonic Bergman space
Xing-Tang Dong1 ; Ze-Hua Zhou1
1 Department of Mathematics Tianjin University Tianjin 300072, P.R. China
Studia Mathematica, Tome 219 (2013) no. 2, pp. 163-175

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

We present here a quite unexpected result: If the product of two quasihomogeneous Toeplitz operators $T_fT_g$ on the harmonic Bergman space is equal to a Toeplitz operator $T_h$, then the product $T_gT_f$ is also the Toeplitz operator $T_h$, and hence $T_f$ commutes with $T_g$. From this we give necessary and sufficient conditions for the product of two Toeplitz operators, one quasihomogeneous and the other monomial, to be a Toeplitz operator.
DOI : 10.4064/sm219-2-6
Keywords: present here quite unexpected result product quasihomogeneous toeplitz operators harmonic bergman space equal toeplitz operator product toeplitz operator hence commutes necessary sufficient conditions product toeplitz operators quasihomogeneous other monomial toeplitz operator

Xing-Tang Dong 1 ; Ze-Hua Zhou 1

1 Department of Mathematics Tianjin University Tianjin 300072, P.R. China 
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Xing-Tang Dong; Ze-Hua Zhou. Product equivalence of quasihomogeneous Toeplitz operators
 on the harmonic Bergman space. Studia Mathematica, Tome 219 (2013) no. 2, pp. 163-175. doi: 10.4064/sm219-2-6

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