Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

Article

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Bull. Korean Math. Soc. 2018; 55(2): 367-378

Online first article January 8, 2018      Printed March 30, 2018

https://doi.org/10.4134/BKMS.b170025

Copyright © The Korean Mathematical Society.

On $m$-isometric Toeplitz operators

Eungil Ko, Jongrak Lee

Ewha Womans University, Ewha Womans University

Abstract

In this paper, we study $m$-isometric Toeplitz operators $T_{\varphi}$ with rational symbols. We characterize $m$-isometric Toeplitz operators $T_{\varphi}$ by properties of the rational symbols $\varphi$. In addition, we give a necessary and sufficient condition for Toeplitz operators $T_{\varphi}$ with analytic symbols $\varphi$ to be $m$-expansive or $m$-contractive. Finally, we give some results for $m$-expansive and $m$-contractive Toeplitz operators $T_{\varphi}$ with trigonometric polynomial symbols $\varphi$.

Keywords: $m$-isometric operators, expansive operators, contractive operators, Toeplitz operators

MSC numbers: 47A62, 47B15, 47B20