School of Mathematical & Statistical Sciences Faculty Publications

Schur product techniques for commuting multivariable weighted shifts

Document Type

Article

Publication Date

9-15-2007

Abstract

In this paper we study the hyponormality and subnormality of 2-variable weighted shifts using the Schur product techniques in matrices. As applications, we generalize the result in [R. Curto, J. Yoon, Jointly hyponormal pairs of subnormal operators need not be jointly subnormal, Trans. Amer. Math. Soc. 358 (2006) 5135-5159, Theorem 5.2] and give a non-trivial, large class satisfying the Curto-Muhly-Xia conjecture [R. Curto, P. Muhly, J. Xia, Hyponormal pairs of commuting operators, Oper. Theory Adv. Appl. 35 (1988) 1-22] for 2-variable weighted shifts. Further, we give a complete characterization of hyponormality and subnormality in the class of flat, contractive, 2-variable weighted shifts T ≡ (T1, T2) with the condition that the norm of the 0th horizontal 1-variable weighted shift of T is a given constant.

Comments

© 2006 Elsevier Inc. All rights reserved. http://www.elsevier.com/open-access/userlicense/1.0/

First Page

626

Last Page

641

Publication Title

Journal of Mathematical Analysis and Applications

DOI

10.1016/j.jmaa.2006.11.040

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