The Fredholm index of quotient Hilbert modules

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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Published 1 January 2005