Journal article
Aluthge transforms of 2-variable weighted shifts
Integral Equations and Operator Theory, Vol.90(5), pp.1-32
06/10/2017
DOI: 10.1007/s00020-018-2475-1
Abstract
Integral equations Operator Theory (2018) 90:52; 33 pp 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.
Details
- Title: Subtitle
- Aluthge transforms of 2-variable weighted shifts
- Creators
- Raul E CurtoJasang Yoon
- Resource Type
- Journal article
- Publication Details
- Integral Equations and Operator Theory, Vol.90(5), pp.1-32
- DOI
- 10.1007/s00020-018-2475-1
- ISSN
- 0378-620X
- eISSN
- 1420-8989
- Grant note
- DOI: 10.13039/100000001, name: National Science Foundation, award: DMS-1302666, DMS-0801168
- Language
- English
- Date published
- 06/10/2017
- Academic Unit
- Mathematics
- Record Identifier
- 9983985960502771
Metrics
26 Record Views