ABSTRACT
In this paper, we review and investigate some properties of a linear pencil in the frame of the point spectrum and an isolated point in its spectrum. We next give relationships among the spectrum of the linear pencil, the Taylor spectrums of a commuting pair and its spherical Aluthge transform through projection maps and the spectral mapping theorem.
2010 MATHEMATICS SUBJECT CLASSIFICATIONS:
Acknowledgments
The authors wish to thank Professor Raul E. Curto for his many valuable suggestions and comments. The authors are deeply grateful to the referee for a careful reading of the paper and for several suggestions and edits that helped to improve the presentation.
Disclosure statement
No potential conflict of interest was reported by the authors.