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

Title & Authors
ON 2-HYPONORMAL TOEPLITZ OPERATORS WITH FINITE RANK SELF-COMMUTATORS
Kim, An-Hyun;

Abstract
Suppose $\small{T_{\varphi}}$ is a 2-hyponormal Toeplitz operator whose self-commutator has rank $\small{n{\geq}1}$. If $\small{H_{\bar{\varphi}}(ker[T^*_{\varphi},T_{\varphi}}$$\small{]}$$\small{)}$ contains a vector $\small{e_n}$ in a canonical orthonormal basis $\small{\{e_k\}_{k{\in}Z_+}}$ of $\small{H^2({\mathbb{T}})}$, then $\small{{\varphi}}$ should be an analytic function of the form $\small{{\varphi}=qh}$, 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;
Language
English
Cited by
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