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Nontrivial invariant subspaces of linear operator pencils

Part of: Special classes of linear operators General theory of linear operators

Published online by Cambridge University Press:  07 June 2023

Jaewoong Kim  and
Jasang Yoon
Jaewoong Kim
Affiliation:
Department of Mathematics, Korea Military Academy, Seoul 01805, Korea e-mail: jaewoongkim@mnd.go.kr
Jasang Yoon*
Affiliation:
School of Mathematical and Statistical Sciences, The University of Texas Rio Grande Valley, Edinburg, TX 78539, USA
*
e-mail: jasang.yoon@utrgv.edu
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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.

Keywords

47A13Linear pencilpolar decompositionAluthge transforminvariant subspaces

MSC classification

Primary: 47A15: Invariant subspaces
Secondary: 47A13: Several-variable operator theory (spectral, Fredholm, etc.) 47A65: Structure theory 47B49: Transformers, preservers (operators on spaces of operators)

Information

Type
Article
Information
Canadian Mathematical Bulletin , Volume 67 , Issue 1 , March 2024 , pp. 1 - 8
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Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of The Canadian Mathematical Society

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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

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