Polar decompositions and spectral properties of linear operator pencils

Authors

Slaviša Djordjević, Benemerita Universidad Autonoma de Puebla
Jaewoong Kim, Korea Military Academy
Jasang Yoon, The University of Texas Rio Grande ValleyFollow

Document Type

Article

Publication Date

2025

Abstract

In this paper, we introduce the spherical polar decomposition of the linear pencil of an ordered pair T=(T1,T2) . Using this decomposition, we define the generalized spherical Aluthge transforms for the linear pencil of an ordered pair T=(T1,T2) and give spectral properties between the linear pencil and the generalized spherical Aluthge transform of it. In detail, we study whether the spectral properties of the linear pencil of an ordered pair T=(T1,T2) are invariant under the generalized spherical Aluthge transform.

Comments

Original published version available at https://doi.org/10.1007/s13398-024-01691-z

Recommended Citation

Djordjević, Slaviša, Jaewoong Kim, and Jasang Yoon. "Polar decompositions and spectral properties of linear operator pencils." Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas 119, no. 1 (2025): 25. https://doi.org/10.1007/s13398-024-01691-z

Publication Title

Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas

DOI

10.1007/s13398-024-01691-z