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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 $M_{z^N}$.
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참고문헌 (7)
참고문헌 신청
Mohammed Albaseer / 2015 / REDUCING SUBSPACES FOR A CLASS OF TOEPLITZ OPERATORS ON THE BERGMAN SPACE OF THE BIDISK / 대한수학회보 52(5):1649~1660
H. Dan / 2014 / Multiplication operators defined by a class of polynomials on L2a(D2) / Integral Equations Operator Theory 80(4):581~601
K. Guo / 2015 / Multiplication operators on the Bergman space / Springer
Y. Lu / 2010 / Invariant subspaces and reducing subspaces of weighted Bergman space over bidisk / J. Math. Soc. Japan 62(3):745~765
L. Shan / 2003 / Reducing subspaces for a class of analytic Toeplitz operators on the bidisc / J. Fudan Univ. Nat. Sci 42(2):196~200
H. Dan / 2014 / Multiplication operators defined by a class of polynomials on L2a(D2) / Integral Equations Operator Theory 80(4):581~601
K. Guo / 2015 / Multiplication operators on the Bergman space / Springer
Y. Lu / 2010 / Invariant subspaces and reducing subspaces of weighted Bergman space over bidisk / J. Math. Soc. Japan 62(3):745~765
L. Shan / 2003 / Reducing subspaces for a class of analytic Toeplitz operators on the bidisc / J. Fudan Univ. Nat. Sci 42(2):196~200
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