Journal of Operator Theory

Volume 62, Issue 2, Fall 2009 pp. 439-452.

Dimension formula for localization of Hilbert Modules

Authors: Yongjiang Duan (1) and Kunyu Guo (2)
Author institution: (1) School of Mathematics and Statistics, Northeast Normal University, Changchun, 130024, China
(2) School of Mathematical Sciences, Fudan University, Shanghai, 200433, China

Summary: This paper considers a conjecture of Douglas, Misra and Varughese about the dimension formula of the localization of an analytic Hilbert submodule generated by polynomials \cite{DMV}. The conjecture states that there exists a relation between the dimension of the localization of an analytic submodule generated by an ideal of polynomials and the codimension of the zero variety of the ideal. It is shown that the conjecture is true in most natural cases. Some examples show that there are exceptions to this conjecture. The results apply here to compute curvature invariants of quotient submodules.

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