Product equivalence of quasihomogeneous Toeplitz operators on the harmonic Bergman space

• Autorzy: Xing-Tang Dong , Ze-Hua Zhou
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 47B35: Toeplitz operators, Hankel operators, Wiener-Hopf operators

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2013
• Tom: 219
• Numer: 2
• Strony: 163-175

Daty

wydano

2013

Twórcy

autor

Xing-Tang Dong

• Department of Mathematics, Tianjin University, Tianjin 300072, P.R. China

autor

Ze-Hua Zhou

• Department of Mathematics, Tianjin University, Tianjin 300072, P.R. China

Identyfikatory

DOI

10.4064/sm219-2-6