# ON 2-HYPONORMAL TOEPLITZ OPERATORS WITH FINITE RANK SELF-COMMUTATORS

Kim, An-Hyun

• Received : 2015.11.01
• Published : 2016.07.31
• 17 6

#### Abstract

Suppose $T_{\varphi}$ is a 2-hyponormal Toeplitz operator whose self-commutator has rank $n{\geq}1$. If $H_{\bar{\varphi}}(ker[T^*_{\varphi},T_{\varphi}])$ contains a vector $e_n$ in a canonical orthonormal basis $\{e_k\}_{k{\in}Z_+}$ of $H^2({\mathbb{T}})$, then ${\varphi}$ should be an analytic function of the form ${\varphi}=qh$, where q is a finite Blaschke product of degree at most n and h is an outer function.

#### Keywords

Toeplitz operators;finite rank self-commutators;subnormal;hyponormal;2-hyponormal

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#### Acknowledgement

Supported by : Changwon National University