Sun Shunhua.ON HYPONORMAL WEIGHTED SHIFT[J].Chinese Annals of Mathematics B,1984,5(1):101~108
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Authors：
Sun Shunhua;
Abstract：
It is shown in this paper that the necessary condition that a hyponormal weighted unilateral shift of norm one be unitarily equivalent to a Toeplitz operator is that the
associated weights $\[\{ {a_n}\} _0^\infty \]$ must stisfy $\[1 - {\left| {{a_n}} \right|^2} = {(1 - {\left| {{a_0}} \right|^2})^{n + 1}}\forall n \ge 0\]$. As a consequence we obtain that the answer to Abrahamse's Problem 3 is that the Bergman shift is not unitarily equivalent to a Toeplitz operator.
