Product equivalence of quasihomogeneous Toeplitz operators on the harmonic Bergman space

Xing-Tang Dong, and Ze-Hua Zhou. "Product equivalence of quasihomogeneous Toeplitz operators on the harmonic Bergman space." Studia Mathematica 219.2 (2013): 163-175. <http://eudml.org/doc/285448>.

@article{Xing2013,
abstract = {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.},
author = {Xing-Tang Dong, Ze-Hua Zhou},
journal = {Studia Mathematica},
keywords = {Toeplitz operators; harmonic Bergman space; quasihomogeneous symbols},
language = {eng},
number = {2},
pages = {163-175},
title = {Product equivalence of quasihomogeneous Toeplitz operators on the harmonic Bergman space},
url = {http://eudml.org/doc/285448},
volume = {219},
year = {2013},
}

TY - JOUR
AU - Xing-Tang Dong
AU - Ze-Hua Zhou
TI - Product equivalence of quasihomogeneous Toeplitz operators on the harmonic Bergman space
JO - Studia Mathematica
PY - 2013
VL - 219
IS - 2
SP - 163
EP - 175
AB - 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.
LA - eng
KW - Toeplitz operators; harmonic Bergman space; quasihomogeneous symbols
UR - http://eudml.org/doc/285448
ER -