Bulletin of the
Korean Mathematical Society
BKMS

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

Article

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Bull. Korean Math. Soc. 2017; 54(2): 633-646

Online first article January 4, 2017      Printed March 31, 2017

https://doi.org/10.4134/BKMS.b160231

Copyright © The Korean Mathematical Society.

Weak and quadratic hyponormality of 2-variable weighted shifts and their examples

Chunji Li

Northeastern University

Abstract

Recently, Curto, Lee and Yoon considered the properties (such as, hyponormality, subnormality, and flatness, etc.) for $2$-variable weighted shifts and constructed several families of commuting pairs of subnormal operators such that each family can be used to answer a conjecture of Curto, Muhly and Xia negatively. In this paper, we consider the weak and quadratic hyponormality of 2-variable weighted shifts $\left( W_{1},W_{2}\right) $. In addition, we detect the weak and quadratic hyponormality with some interesting 2-variable weighted shifts.

Keywords: weakly hyponormal, quadratically hyponormal, 2-variable weighted shifts

MSC numbers: Primary 47B37; Secondary 47B20