Approximation by invertible and noninvertible operators (Q1120768)

Let T be a bounded linear operator on a complex separable Hilbert space. The author considers the approximation of T by operators with unequal kernel dimension and determines \(\inf \{\| T-S\|:\) dim ker \(S\neq \dim \ker T\}\). This problem is related to that of approximating T by invertible operators and by noninvertible operators.