The Flatness Property of Local-cubically Hyponormal Weighted Shifts

Seunghwan Baek; Hyunjin Do; Mi Ryeong Lee; Chunji Li

doi:10.5666/KMJ.2019.59.2.315

Article

KYUNGPOOK Math. J. 2019; 59(2): 315-324

Published online June 23, 2019

The Flatness Property of Local-cubically Hyponormal Weighted Shifts

Seunghwan Baek and Hyunjin Do, Mi Ryeong Lee^∗,Chunji Li

Department of Mathematics, Kyungpook National University, Daegu 41566, Korea
e-mail : seunghwan@knu.ac.kr and jinjinyy@daum.net

Institute of Liberal Education, Daegu Catholic University, Gyeongsan, Gyeongbuk 38430, Korea
e-mail : leemr@cu.ac.kr

Department of Mathematics, Northeastern University, Shenyang 110819, P. R. China
e-mail : lichunji@mail.neu.edu.cn

Received: October 16, 2018; Accepted: February 20, 2019

Abstract

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Abstract

In this note we introduce a local-cubically hyponormal weighted shift of order θ with 0≤θ≤π2, which is a new notion between cubic hyponormality and quadratic hyponormality of operators. We discuss the property of flatness for local-cubically hyponormal weighted shifts.

Keywords: quadratically hyponormal, cubically hyponormal, weighted shifts.