Product equivalence of quasihomogeneous Toeplitz operators on the harmonic Bergman space

Xing-Tang Dong; Ze-Hua Zhou

Studia Mathematica, Tome 215 (2013), p. 163-175 / Harvested from The Polish Digital Mathematics Library

Résumé

We present here a quite unexpected result: If the product of two quasihomogeneous Toeplitz operators $T_{f} T_{g}$ on the harmonic Bergman space is equal to a Toeplitz operator $T_{h}$ , then the product $T_{g} T_{f}$ 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.

Publié le : 2013-01-01

Zbl 1310.47041

EUDML-ID : urn:eudml:doc:285448

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     title = {Product equivalence of quasihomogeneous Toeplitz operators on the harmonic Bergman space},
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     year = {2013},
     pages = {163-175},
     zbl = {1310.47041},
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Xing-Tang Dong; Ze-Hua Zhou. Product equivalence of quasihomogeneous Toeplitz operators on the harmonic Bergman space. Studia Mathematica, Tome 215 (2013) pp. 163-175. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm219-2-6/