JOURNAL BROWSE
Search
Advanced SearchSearch Tips
REDUCING SUBSPACES FOR A CLASS OF TOEPLITZ OPERATORS ON THE BERGMAN SPACE OF THE BIDISK
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
REDUCING SUBSPACES FOR A CLASS OF TOEPLITZ OPERATORS ON THE BERGMAN SPACE OF THE BIDISK
ALBASEER, MOHAMMED; LU, YUFENG; SHI, YANYUE;
  PDF(new window)
 Abstract
In this paper, we completely characterize the nontrivial reducing subspaces of the Toeplitz operator on the Bergman space , where N and M are positive integers.
 Keywords
reducing subspace;Toeplitz operator;polydisk;
 Language
English
 Cited by
1.
Reducing subspaces for a class of non-analytic Toeplitz operators on the bidisk, Journal of Mathematical Analysis and Applications, 2017, 445, 1, 784  crossref(new windwow)
 References
1.
H. Dan, and H. Huang, Multiplication operators defined by a class of polynomials on $L^2_{\alpha}({\mathbb{D}}^2)$, Integral Equations Operator Theory 80 (2014), no. 4, 581-601. crossref(new window)

2.
R. G. Douglas, M. Putinar, and K. Wang, Reducing subspaces for analytic multipliers of the Bergman space, J. Funct. Anal. 263 (2012), no. 6, 1744-1765. crossref(new window)

3.
R. G. Douglas, S. Sun, and D. Zheng, Multiplication operators on the Bergman space via analytic continuation, Adv. Math. 226 (2011), no. 1, 541-583. crossref(new window)

4.
K. Guo and H. Huang, On multiplication operators on the Bergman space: Similarity, unitary equivalence and reducing subspaces, J. Operator Theory 65 (2011), no. 2, 355-378.

5.
K. Guo and H. Huang, Multiplication operators defined by covering maps on the Bergman space: the connection between operator theory and von Neumann algebras, J. Funct. Anal. 260 (2011), no. 4, 1219-1255. crossref(new window)

6.
K. Guo and H. Huang, Geometric constructions of thin Blaschke products and reducing subspace problem, Proc. Lond. Math. Soc. 109 (2014), no. 4, 1050-1091. crossref(new window)

7.
K. Guo and H. Huang, Multiplication Operators on the Bergman Space, Lecture Notes in Mathematics 2145, Springer-Verlag Berlin Heidelberg 2015.

8.
K. Guo, S. Sun, D. Zheng, and C. Zhong, Multiplication operators on the Bergman space via the Hardy space of the bidisk, J. Reine Angew. Math. 628 (2009), 129-168.

9.
J. Hu, S. Sun, X. Xu, and D. Yu, Reducing subspace of analytic Toeplitz operators on the Bergman space, Integral Equations Operator Theory 49 (2004), no. 3, 387-395. crossref(new window)

10.
Y. Lu and X. Zhou, Invariant subspaces and reducing subspaces of weighted Bergman space over bidisk, J. Math. Soc. Japan 62 (2010), no. 3, 745-765. crossref(new window)

11.
Y. Shi and Y. Lu, Reducing subspaces for Toeplitz operators on the polydisk, Bull. Korean Math. Soc. 50 (2013), no. 2, 687-696. crossref(new window)

12.
M. Stessin and K. Zhu, Reducing subspaces of weighted shift operators, Proc. Amer. Math. Soc. 130 (2002), no. 9, 2631-2639. crossref(new window)

13.
S. L. Sun and Y. Wang, Reducing subspaces of certain analytic Toeplitz operators on the Bergman space, Northeast. Math. J. 14 (1998), no. 2, 147-158.

14.
S. Sun, D. Zheng, and C. Zhong, Classification of reducing subspaces of a class of multiplication operators on the Bergman space via the Hardy space of the bidisk, Canad. J. Math. 62 (2010), no. 2, 415-438. crossref(new window)

15.
X. Wang, H. Dan, and H. Huang, Reducing subspaces of multiplication operators with the symbol ${\alpha}z^k$ +${\beta}w^l$ on $L^2_{\alpha}({\mathbb{D}}^2)$, Sci. China Math. 58 (2015), doi:10.1007/s11425-015-4973-9. crossref(new window)

16.
K. Zhu, Reducing subspaces for a class of multiplication operators, J. Lond. Math. Soc. 62 (2000), no. 2, 553-568. crossref(new window)