Journal article
Quasinormality of powers of commuting pairs of bounded operators
Journal of functional analysis, Vol.278(3), p.108342
02/01/2020
DOI: 10.1016/j.jfa.2019.108342
Abstract
We study jointly quasinormal and spherically quasinormal pairs of commuting operators on Hilbert space, as well as their powers. We first prove that, up to a constant multiple, the only jointly quasinormal 2-variable weighted shift is the Helton-Howe shift. Second, we show that a left invertible subnormal operator T whose square T2 is quasinormal must be quasinormal. Third, we generalize a characterization of quasinormality for subnormal operators in terms of their normal extensions to the case of commuting subnormal n-tuples. Fourth, we show that if a 2-variable weighted shift W(α,β) and its powers W(α,β)(2,1) and W(α,β)(1,2) are all spherically quasinormal, then W(α,β) may not necessarily be jointly quasinormal. Moreover, it is possible for both W(α,β)(2,1) and W(α,β)(1,2) to be spherically quasinormal without W(α,β) being spherically quasinormal. Finally, we prove that, for 2-variable weighted shifts, the common fixed points of the toral and spherical Aluthge transforms are jointly quasinormal.
Details
- Title: Subtitle
- Quasinormality of powers of commuting pairs of bounded operators
- Creators
- Raúl E Curto - University of IowaSang Hoon Lee - Chungnam National UniversityJasang Yoon - The University of Texas Rio Grande Valley
- Resource Type
- Journal article
- Publication Details
- Journal of functional analysis, Vol.278(3), p.108342
- Publisher
- Elsevier Inc
- DOI
- 10.1016/j.jfa.2019.108342
- ISSN
- 0022-1236
- eISSN
- 1096-0783
- Grant note
- University of Texas System (https://doi.org/10.13039/100007130) Consejo Nacional de Ciencia y Tecnología (https://doi.org/10.13039/501100003141) DMS-1302666 / NSF (https://doi.org/10.13039/100000001) 2016R1D1A1B03933776 / NRF (https://doi.org/10.13039/501100003725)
- Language
- English
- Date published
- 02/01/2020
- Academic Unit
- Mathematics
- Record Identifier
- 9984240866802771
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