The closed range points and quasi-similarity of weighted shift operators of degree \(K\) (Q1200695)

In his dissertation (1970), \textit{A. Lambert} has proved that two quasi- similar injective unilateral weighted shifts must be similar and hence have the same closed range points. He left open the question whether the conclusion is true for injective bilateral weighted shift operators. The author has answered this question affirmatively with a stronger result. Further, the author has also shown that two quasi-similar injective bilateral weighted shifts of degree \(K\) have the same closed range points hence have equal essential spectra and that two quasi-similar dominant bilateral weighted shifts have the same closed range points and equal stable spectra.