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Suppose $T_\varphi$ is a $2$--hyponormal Toeplitz operator whose self--commutator has rank $n\ge 1$. If $H_{\bar\varphi}\left(\ker\,[T_\varphi^*, T_\varphi]\right)$ contains a vector $e_n$ in a canonical orthonormal basis $\{e_k\}_{k\in \mathbb Z_+}$ of $H^2(\mathbb T)$, then $\varphi$ should be an analytic function of the form $\varphi=q h$, where $q$ is a finite Blaschke product of degree at most $n$ and $h$ is an outer function.
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참고문헌 (23)
참고문헌 신청
M. B. Abrahamse / 1976 / Subnormal Toeplitz operators and functions of bounded type / Duke Math. J 43(3):597~604
A. Aleman / 1996 / Subnormal operators with compact selfcommutator / Manuscripta Math 91(3):353~367
I. Amemiya / 1975 / On quasinormal Toeplitz operators / Proc. Amer. Math. Soc 50:254~258
J. Bram / 1955 / Subnormal operators / Duke Math. J 22:75~94
A. Brown / 1964 / Algebraic properties of Toeplitz operators / J. Reine Angew. Math 213:89~102
A. Aleman / 1996 / Subnormal operators with compact selfcommutator / Manuscripta Math 91(3):353~367
I. Amemiya / 1975 / On quasinormal Toeplitz operators / Proc. Amer. Math. Soc 50:254~258
J. Bram / 1955 / Subnormal operators / Duke Math. J 22:75~94
A. Brown / 1964 / Algebraic properties of Toeplitz operators / J. Reine Angew. Math 213:89~102
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