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This paper mainly considers a tuple of multiplication operators on Bergman spaces over polydisks which essentially arise from a matrix, their joint reducing subspaces and associated von Neumann algebras. It is shown that there is an interesting link of the non-triviality for such von Neumann algebras with the determinant of the matrix. A complete characterization of their abelian property is given under a more general setting.
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참고문헌 (21)
참고문헌 신청
C. Cowen / 1978 / The commutant of an analytic Toeplitz operator / Trans. Amer. Math. Soc. 239:1~31
C. Cowen / 1980 / The commutant of an analytic Toeplitz operator. II / Indiana Univ. Math. J. 29(1):1~12
C. Cowen / 1980 / An analytic Toeplitz operator that commutes with a compact operator and a related class of Toeplitz operators / J. Funct. Anal. 36(2):169~184
H. Dan / 2014 / Multiplication operators de ned by a class of polynomials on $L^^2_a({\mathbb{D}}^2)$ / Integral Equations Operator Theory 80(4):581~601
R. Douglas / 2012 / Reducing subspaces for analytic multipliers of the Bergman space / J. Funct. Anal. 263(6):1744~1765
C. Cowen / 1980 / The commutant of an analytic Toeplitz operator. II / Indiana Univ. Math. J. 29(1):1~12
C. Cowen / 1980 / An analytic Toeplitz operator that commutes with a compact operator and a related class of Toeplitz operators / J. Funct. Anal. 36(2):169~184
H. Dan / 2014 / Multiplication operators de ned by a class of polynomials on
R. Douglas / 2012 / Reducing subspaces for analytic multipliers of the Bergman space / J. Funct. Anal. 263(6):1744~1765
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