Fredholm spectrum and growth of cohomology groups
Let T ∈ L(E)ⁿ be a commuting tuple of bounded linear operators on a complex Banach space E and let be the non-essential spectrum of T. We show that, for each connected component M of the manifold of all smooth points of , there is a number p ∈ 0, ..., n such that, for each point z ∈ M, the dimensions of the cohomology groups grow at least like the sequence with d = dim M.