Abstract
A condition is given on a set Ol of operators on Hilbert space that guarantees it has the following property: For any Fredholm operator T of index zero there exists an Aϵ A such that T + ϵA is invertible for all sufficiently small nonzero ϵ. As a corollary one obtains in a quite general setting the density of the invertible Toeplitz operators in the set of Fredholm Toeplitz operators of index zero.
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