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On $2$--hyponormal Toeplitz operators with finite rank self--commutators

김안현
대한수학회 (The Korean Mathematical Society)|2016.07|대한수학회논문집 (Communications of the KMS)|제31권 제3호|pp. 585-590

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참고문헌

키워드

Toeplitz operatorshyponormalfinite rank self-commutatorssubnormal2--hyponormal
주제분류수학

초록

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.

Abstract

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.

참고문헌 (23)

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