Abstract
The formula for the distance from a given operator to the invertible operators on a separable Hilbert space is not true if the underlying Hilbert space is not required to be separable. This paper obtains inequalities for that distance in the latter situation. This requires a new concept called the modulus of invertibility, and further study of the concepts of essential nullity and essential deficiency, which permitted us to characterize the closure of the invertible operators.
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