[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/CKMS.c150201

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

Kim, An-Hyun (Department of Mathematics Changwon National University)

Publication Information

Communications of the Korean Mathematical Society / v.31, no.3, 2016 , pp. 585-590 More about this Journal

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;

Citations & Related Records

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