complex analysis；
functional analysis；
operator theory；
complex geometry；
linear dynamic system
Main publications:
Yong-Xin Gao and Ze-Hua Zhou, “Spectra of some invertible weighted composition operators on Hardy and weighted Bergman spaces in the unit ball”, In this paper, we investigate the spectra of invertible weighted composition operators with automorphism symbols, on Hardy space $H^2(\mathbb{B}_N)$ and weighted Bergman spaces $A_\alpha^2(\mathbb{B}_N)$, where $\mathbb{B}_N$ is the unit ball of the
$N$-dimensional complex space. By taking $N=1$, $\mathbb{B}_N=\mathbb{D}$ the unit disc, we also complete the discussion about the spectrum of a weighted composition operator when it is invertible on $H^2(\mathbb{D})$ or $A_\alpha^2(\mathbb{D})$., Ann. Acad. Sci. Fenn. Math., 41:1 (2016), 177-198
Yu-Xia Liang and Ze-Hua Zhou, “Supercyclic translation $C_0$-semigroup on complex sectors”, We characterize the supercyclic behavior of sequences of operators in a $C_0$-semigroup whose index set is a sector $\Delta$ in the complex plane $\mathbb{C}$., Discrete Contin. Dyn. Syst., 36:1 (2016), 361-370
Zhong-Shan Fang and Ze-Hua Zhou, “Disjoint Mixing Linear Fractional Composition Operators in the Unit Ball”, In the present paper we investigate the disjoint mixing property of finitely many linear fractional composition operators acting on the space of holomorphic functions on the unit ball in $\mathbb{C}^N,$ and generalize parts of the results obtained by Bès, Martin and Peris in 2011., C. R. Math. Acad. Sci. Paris, 353:10 (2015), 937-942
Ce-Zhong Tong and Ze-Hua Zhou, “Intertwining relations for Volterra operators on the Bergman space”, On the Bergman space in the unit disk, we study the intertwining relation
for Volterra type operators, whose intertwining operator is a composition operator.
We also investigate the "compact"
intertwining relations for Volterra type operators. As obvious
consequences, the essential commutativity of Volterra type
and composition operators are characterized. At the end of the paper,
we find a new connection between the Bergman space and little Bloch space through this essential commutativity., Illinois J. Math., 57:1 (2013), 195-211
Xing-Tang Dong and Ze-Hua Zhou, “roduct equivalence of quasihomogeneous Toeplitz operators on the harmonic Bergman space”, 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 $T_gT_f$ also is the Toeplitz operator $T_h$, and hence $T_f$ must commute 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., Studia Math., 219:2 (2013), 163-175
