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REDUCING SUBSPACES FOR TOEPLITZ OPERATORS ON THE POLYDISK
Shi, Yanyue,Lu, Yufeng Korean Mathematical Society 2013 대한수학회보 Vol.50 No.2
In this note, we completely characterize the reducing subspaces of $T_{{z^N_1}{z^M_2}}$ on $A^2_{\alpha}(D^2)$ where ${\alpha}$ > -1 and N, M are positive integers with $N{\neq}M$, and show that the minimal reducing subspaces of $T_{{z^N_1}{z^M_2}}$ on the unweighted Bergman space and on the weighted Bergman space are different.
Reducing subspaces for Toeplitz operators on the polydisk
Yanyue Shi,Yufeng Lu 대한수학회 2013 대한수학회보 Vol.50 No.2
In this note, we completely characterize the reducing sub- spaces of TzN 1 zM 2 on A2 α(D2) where α> −1 and N,M are positive in- tegers with N ≠ M, and show that the minimal reducing subspaces of TzN 1 zM 2 on the unweighted Bergman space and on the weighted Bergman space are different.
Reducing subspaces of a class of multiplication operators
Bin Liu,Yanyue Shi 대한수학회 2017 대한수학회보 Vol.54 No.4
Let $M_{z^N}$($N\in \mathbb{Z}_+^d$) be a bounded multiplication operator on a class of Hilbert spaces with orthogonal basis $\{z^n: n\in \mathbb{Z}_+^d\}$. In this paper, we prove that each reducing subspace of $M_{z^N}$ is the direct sum of some minimal reducing subspaces. For the case that $d=2$, we find all the minimal reducing subspaces of $M_{z^N}(N=(N_1,N_2), N_1\neq N_2)$ on weighted Bergman space $A_\alpha^2(\mathbb{B}_2)(\alpha>-1)$ and Hardy space $H^2(\mathbb{B}_2)$, and characterize the structure of $\mathcal{V}^*(z^N)$, the commutant algebra of the von Neumann algebra generated by $M_{z^N}$.
REDUCING SUBSPACES OF A CLASS OF MULTIPLICATION OPERATORS
Liu, Bin,Shi, Yanyue Korean Mathematical Society 2017 대한수학회보 Vol.54 No.4
Let $M_{z^N}(N{\in}{\mathbb{Z}}^d_+)$ be a bounded multiplication operator on a class of Hilbert spaces with orthogonal basis $\{z^n:n{\in}{\mathbb{Z}}^d_+\}$. In this paper, we prove that each reducing subspace of $M_{z^N}$ is the direct sum of some minimal reducing subspaces. For the case that d = 2, we find all the minimal reducing subspaces of $M_{z^N}$ ($N=(N_1,N_2)$, $N_1{\neq}N_2$) on weighted Bergman space $A^2_{\alpha}({\mathbb{B}}_2)$(${\alpha}$ > -1) and Hardy space $H^2({\mathbb{B}}_2)$, and characterize the structure of ${\mathcal{V}}^{\ast}(z^N)$, the commutant algebra of the von Neumann algebra generated by $M_{z^N}$.
THE HYPONORMAL TOEPLITZ OPERATORS ON THE VECTOR VALUED BERGMAN SPACE
Lu, Yufeng,Cui, Puyu,Shi, Yanyue Korean Mathematical Society 2014 대한수학회보 Vol.51 No.1
In this paper, we give a necessary and sufficient condition for the hyponormality of the block Toeplitz operators $T_{\Phi}$, where ${\Phi}$ = $F+G^*$, F(z), G(z) are some matrix valued polynomials on the vector valued Bergman space $L^2_a(\mathbb{D},\mathbb{C}^n)$. We also show some necessary conditions for the hyponormality of $T_{F+G^*}$ with $F+G^*{\in}h^{\infty}{\otimes}M_{n{\times}n}$ on $L^2_a(\mathbb{D},\mathbb{C}^n)$.
REDUCING SUBSPACES FOR A CLASS OF TOEPLITZ OPERATORS ON THE BERGMAN SPACE OF THE BIDISK
Mohammed Albaseer,Yufeng Lu,Yanyue Shi 대한수학회 2015 대한수학회보 Vol.52 No.5
In this paper, we completely characterize the nontrivial reducing subspaces of the Toeplitz operator TzN 1- zM2 on the Bergman space A2(D2), where N and M are positive integers.
The Hyponormal Toeplitz operators on the vector valued Bergman space
Yufeng Lu,Puyu Cui,Yanyue Shi 대한수학회 2014 대한수학회보 Vol.51 No.1
In this paper, we give a necessary and sufficient condition for the hyponormality of the block Toeplitz operators TΦ, where Φ = F +G∗, F(z), G(z) are some matrix valued polynomials on the vector valued Bergman space L2 a(D, Cn). We also show some necessary conditions for the hyponormality of TF+G* with F + G∗ 2 h∞ ⓧ Mn×n on L2 a(D, Cn). In this paper, we give a necessary and sufficient condition for the hyponormality of the block Toeplitz operators TΦ, where Φ = F +G∗, F(z), G(z) are some matrix valued polynomials on the vector valued Bergman space L2 a(D, Cn). We also show some necessary conditions for the hyponormality of TF+G* with F + G∗ ∈ h∞ ⓧ Mn×n on L2 a(D, Cn).
REDUCING SUBSPACES FOR A CLASS OF TOEPLITZ OPERATORS ON THE BERGMAN SPACE OF THE BIDISK
ALBASEER, MOHAMMED,LU, YUFENG,SHI, YANYUE Korean Mathematical Society 2015 대한수학회보 Vol.52 No.5
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.