Mathematical Research Letters

Volume 12, Issue 6, November 2005 pp. 911-920.

The Fredholm index of quotient Hilbert modules

Authors: Xiang Fang
Author institution: University of Alabama

Summary: We show that the (multivariable) Fredholm index of a broad class of quotient Hilbert modules can be calculated by the Samuel multiplicity. These quotient modules include the Hardy, Bergman, or symmetric Fock spaces in several variables modulo submodules generated by multipliers. Our calculation is based on Gleason, Richter, Sundberg's results on the Fredholm index of the corresponding submodules.

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