Aluthge Transforms of 2-Variable Weighted Shifts

Authors

Raul E. Curto, University of Iowa
Jasang Yoon, The University of Texas Rio Grande ValleyFollow

Document Type

Article

Publication Date

7-18-2018

Abstract

We introduce two natural notions of multivariable Aluthge transforms (toral and spherical), and study their basic properties. In the case of 2-variable weighted shifts, we first prove that the toral Aluthge transform does not preserve (joint) hyponormality, in sharp contrast with the 1-variable case. Second, we identify a large class of 2-variable weighted shifts for which hyponormality is preserved under both transforms. Third, we consider whether these Aluthge transforms are norm-continuous. Fourth, we study how the Taylor and Taylor essential spectra of 2-variable weighted shifts behave under the toral and spherical Aluthge transforms; as a special case, we consider the Aluthge transforms of the Drury–Arveson 2-shift. Finally, we briefly discuss the class of spherically quasinormal 2-variable weighted shifts, which are the fixed points for the spherical Aluthge transform.

Comments

© Springer International Publishing AG, part of Springer Nature 2018

Recommended Citation

Curto, Raúl E., and Jasang Yoon. "Aluthge transforms of 2-variable weighted shifts." Integral Equations and Operator Theory 90 (2018): 1-32. https://doi.org/10.1007/s00020-018-2475-1

Publication Title

Integral Equations and Operator Theory

DOI

10.1007/s00020-018-2475-1