# Dechao Zheng

Professor

#### Research Interests

Functional Analysis, Operator Theory, Complex Analysis, Harmonic Analysis.

#### Publications

**Rudin orthogonality problem on the Bergman space**(with**K. Guo**),261 (2011), no. 1, 51–68.

J. Functional Analysis .

**Compact Operators and Toeplitz algebras on Multiply-Connected Domains**(with**M. Jovovic**),, 261 (2011), no. 1, 25–50.

J. Functional Analysis

**Multiplication Operators on the Bergman Space via analytic continuation**(with**R. Douglas and S. Sun**),226 (2011), no. 1, 541–583.

Adv. Math.,

**Similarity of Analytic Toeplitz Operators on the Bergman Spaces**(**C. Jiang**),258 (2010), 2961--2982.

J. Functional Analysis,

**Spectrum and essential spectrum of Toeplitz operators on the Bergman space**(with**C. Sundberg**),

Indiana Univ. Math. J.,*59 (2010), 385--394.*

**Classification of reducing subspaces of a class of multiplication operators on the Bergman space via the Hardy space of the bidisk (with S. Sun and C. Zhong),**

Canad. J. Math.,*62 (2010), 415--438.*

**Compact composition operators on BMOA and the Bloch space**(with**H. Wulan and K. Zhu**)137 (2009), no 11, 3861–3868.

Proc. Amer. Math. Soc,

**Beurling type theorem on the Bergman space via the Hardy space of the bidisk****(with Shunhua Sun),**52 (2009), 2517-2529.

Sci. China Ser. A,

**Multiplication Operators on the Bergman Space via the Hardy Space of the bidisk****(with K. Guo, S. Sun, and C. Zhong),**

J. Reine Angew. Math*.,*628 (2009), 129-168.

**Finite Rank Commutator of Toeplitz Operators or Hankel Operators (with Xuanhao Ding),**(2008), 1099-1119.., 34

Houston J. Math

**Multiplication Operators on the Bergman Space and Weighted shifts****(with S. Sun and C. Zhong),**59(2008), 435-454.

J. Operator Theory,

**Bounded Toeplitz Products on Weighted Bergman Spaces****(with Karel Stroethoff),**59 (2008), 277-308.,

J. Operator Theory

**Finite Rank Commutators and Semicommutators of Toeplitz Operators with Harmonic Symbols (with K. Guo and S. Sun),**

Illinois J. Math.,**51 (2007), no. 2, 583—596.**

**Bounded Toeplitz products on Bergman spaces of the unit ball (with K. Stroethoff),**

J.*Math.**Anal. Appl.,*325(2007), 114-129.

**Toeplitz Algebras on the Disk (with Sheldon Axler)**243 (2007), 67-86.

Journal of Functional Analysis

**Products of Bergman Space Toeplitz operators on the polydisk (with B. R. Choe, Y. J. Lee and K. Nam),**337(2007), 295-316.

Math. Ann.

**m-Berezin transform on the polydisk (with K. Nam),**

*Integral Equations Operator Theory*56 (2006), no. 1, 93--113.

**m-Berezin transform and compact operators (with K. Nam and C. Zhong),**

*Revista**Mat.**Iberoamericana 22(2006), 867-892.*

**Compact perturbations of Hankel Operators (with X. Chen, K. Guo and K. Izuchi) (pdf)**

*J.**Reine Angew**. Math.*578(2005), 1-48.

**Sampling sets and closed range composition operators on the Bloch space (with P. Ghatage; N. Zorboska),(pdf)**

*Proc.**Amer. Math.**Soc.*133(2005), 1371--1377.

**The distribution function inequality for a finite sum of finite products of Toeplitz operators (with K. Guo),**

*J. Functional Analysis.*218 (2005), 1--53. (pdf)

**Standard deviation and Schatten class Hankel operators on the Segal-Bargman space (J. Xia), (pdf)**

*Indiana Univ. Math. J.*53(2004), 1381--1399.

**Hyperbolic derivatives and generalized Schwarz-Pick estimates (with P. Ghatage),(pdf)**

*Proc.**Amer. Math.**Soc.*132 (2004), 3309--3318.

**Compact operators on Bergman spaces (with Jie Miao), (pdf)**

*Integral Equations Operator Theory,*48(2004), 61-79.

**Composition operators on Bergman spaces (with John Clifford), (pdf)**

*Chinese Ann. Math,*24B(2003), 433-448.

**Essentially commuting Hankel and Toeplitz operators (with K. Guo), (pdf)**

*J. Functional Analysis,*201(2003), 121-147.

**Bounded Toeplitz products on the Bergman space of the polydisk (with K. Stroethoff), (pdf)**

*Journal of Mathematical Analysis and Applications,*278 (2003), 125--135.

**Toeplitz algebra and Hankel algebra on the harmonic Bergman space (with K. Guo), (pdf)**

*Journal of Mathematical Analysis and Applications,*276(2002), 213-230.

**Invertible Toeplitz Products (with K. Stroethoff), (pdf)**

*J. Functional Analysis,*195(2002), 48-70.

**Algebraic and Spectral Properties of Dual Toeplitz Operators (with K. Stroethoff), (pdf)**

*Trans.**Amer. Math.**Soc.*354 (2002), 2495--2520.

**Isolated points and essential components of composition operators on $H^infty$ (with T. Hosokawa; K. Izuchi),(pdf)**

*Proc.**Amer. Math.**Soc.*130 (2002), 1765--1773.

**Invariant subspaces, quasi-invariant subspaces, and Hankel operators (with Kunyu Guo), (pdf)**

*J. Functional Analysis*187 (2001), 308--342.