Remarks on “Operators with inverses similar to their adjoints”
Charles R. DePrima · Proceedings of the American Mathematical Society · 1974
A result in the cited paper [ 7 ] which purports to furnish a sufficient condition for an operator T T on a Hilbert space H \mathfrak {H} for which T − 1 S = S T ∗ {T^{ - 1}}S = S{T^ \ast } with 0 ∉ cl ( W ( S ) ) 0 otin \operatorname {cl} (W(S)) to be unitary is shown to be false. Various conditions under which such a result does hold are explored.