Browse > Article
http://dx.doi.org/10.4134/BKMS.2015.52.5.1649

REDUCING SUBSPACES FOR A CLASS OF TOEPLITZ OPERATORS ON THE BERGMAN SPACE OF THE BIDISK  

ALBASEER, MOHAMMED (SCHOOL OF MATHEMATICAL SCIENCES DALIAN UNIVERSITY OF TECHNOLOGY)
LU, YUFENG (SCHOOL OF MATHEMATICAL SCIENCES DALIAN UNIVERSITY OF TECHNOLOGY)
SHI, YANYUE (SCHOOL OF MATHEMATICAL SCIENCES OCEAN UNIVERSITY OF CHINA)
Publication Information
Bulletin of the Korean Mathematical Society / v.52, no.5, 2015 , pp. 1649-1660 More about this Journal
Abstract
In this paper, we completely characterize the nontrivial reducing subspaces of the Toeplitz operator $T{_{z{^N_1{\bar{z}}^M_2}}$ on the Bergman space $A^2(\mathbb{D}^2)$, where N and M are positive integers.
Keywords
reducing subspace; Toeplitz operator; polydisk;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
연도 인용수 순위
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.   DOI   ScienceOn
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.   DOI   ScienceOn
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.   DOI   ScienceOn
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.   DOI   ScienceOn
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.   DOI   ScienceOn
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.   DOI
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.   DOI
11 Y. Shi and Y. Lu, Reducing subspaces for Toeplitz operators on the polydisk, Bull. Korean Math. Soc. 50 (2013), no. 2, 687-696.   DOI   ScienceOn
12 M. Stessin and K. Zhu, Reducing subspaces of weighted shift operators, Proc. Amer. Math. Soc. 130 (2002), no. 9, 2631-2639.   DOI   ScienceOn
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.   DOI   ScienceOn
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.   DOI
16 K. Zhu, Reducing subspaces for a class of multiplication operators, J. Lond. Math. Soc. 62 (2000), no. 2, 553-568.   DOI