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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)