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Nontrivial invariant subspaces of linear operator pencils
Published online by Cambridge University Press: 07 June 2023
Abstract
In this paper, we introduce the spherical polar decomposition of the linear pencil of an ordered pair 
$\mathbf {T}=(T_{1},T_{2})$ and investigate nontrivial invariant subspaces between the generalized spherical Aluthge transform of the linear pencil of 
$\mathbf {T}$ and the linear pencil of the original pair 
$\mathbf {T}$ of bounded operators with dense ranges.
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- © The Author(s), 2023. Published by Cambridge University Press on behalf of The Canadian Mathematical Society
Footnotes
This material is based upon work supported by a grant from the University of Texas System and the Consejo Nacional de Ciencia y Tecnolog ía de México (CONACYT)
References
Aluthge, A.,
On
$p$
-hyponormal operators for
$0<p<1$
. Integr. Equ. Oper. Theory 13(1990), 307–315.CrossRefGoogle Scholar
$p$
-hyponormal operators for
$0<p<1$
. Integr. Equ. Oper. Theory 13(1990), 307–315.CrossRefGoogle ScholarBenhida, C., Curto, R., Lee, S. H., and Yoon, J.,
The spectral picture and joint spectral radius of the generalized spherical Aluthge transforms
. Adv. Math. 408(2022), 108602.CrossRefGoogle Scholar
Bōgli, S. and Marletta, M.,
Essential numerical ranges for linear operator pencils
. IMA J. of Numer. Anal. 40(2020), 2256–2308.CrossRefGoogle Scholar
Cho, M., Jung, I., and Lee, W. Y.,
On the iterated Duggal transform
. Kyungpook Math. J. 49(2009), 647–650.CrossRefGoogle Scholar
Curto, R. and Yoon, J.,
Aluthge transforms of
$2$
-variable weighted shifts
. Integr. Equ. Oper. Theory 90(2018), Article no. 52, 32 pp.CrossRefGoogle Scholar
$2$
-variable weighted shifts
. Integr. Equ. Oper. Theory 90(2018), Article no. 52, 32 pp.CrossRefGoogle ScholarCurto, R. and Yoon, J.,
Spherical Aluthge transforms and quasinormality for commuting pairs of operators
. In: Analysis of operators on function spaces (the Serguei Shimorin memorial volume), Trends in Mathematics, Birkhäuser, Cham, 2019, pp. 213–237.CrossRefGoogle Scholar
Djordjević, S., Kim, J., and Yoon, J.,
Spectra of the spherical Aluthge transform, the linear pencil, and a commuting pair of operators
. Linear Multilinear Algebra 70(2022), 2047–2064.CrossRefGoogle Scholar
Djordjević, S., Kim, J., and Yoon, J., Generalized spherical Aluthge transforms and binormality for commuting pairs of operators. Math. Nachr., to appear. (in press).Google Scholar
Exner, G.,
Aluthge transforms and n-contractivity of weighted shifts
. J. Operator Theory 61(2009), 419–438.Google Scholar
Ito, M., Yamazaki, T., and Yanagida, M.,
On the polar decomposition of the Aluthge transformation and related results
. J. Operator Theory 51(2004), 303–319.Google Scholar
Jung, I., Ko, E., and Pearcy, C.,
Aluthge transform of operators
. Integr. Equ. Oper. Theory 37(2000), 437–448.CrossRefGoogle Scholar
Kim, J. and Yoon, J.,
Aluthge transforms and common invariant subspaces for a commuting
$n$
-tuple of operators
. Integr. Equ. Oper. Theory 87(2017), 245–262.CrossRefGoogle Scholar
$n$
-tuple of operators
. Integr. Equ. Oper. Theory 87(2017), 245–262.CrossRefGoogle ScholarKim, J. and Yoon, J.,
Taylor spectra and common invariant subspaces through the Duggal and generalized Aluthge transforms for commuting n-tuples of operators
. J. Operator Theory 81(2019), 81–105.CrossRefGoogle Scholar