Spherical Aluthge transform, spherical p and log-hyponormality of commuting pairs of operators II

Authors

• Hyung Won Kim, The University of Texas Rio Grande Valley
• Jaewoong Kim, Korea Military Academy
• Jasang Yoon, The University of Texas Rio Grande ValleyFollow

Document Type

Article

Publication Date

2023

Abstract

In this paper, we consider the notions of spherical p, log, and w-hyponormality of commuting pairs of operators and study their properties and relations. We first show that spherically p-hyponormal 2-variable weighted shifts of hyponormal operators are invariant under powers and the generalized spherical Aluthge transformation. Second, we study the relation between spherical p-hyponormality and spherical w-hyponormality. Third, we study whether the spherical p-hyponormality with 0<p< 1 is invariant under the spherical Aluthge transformation. Finally, we briefly discuss the relation between log-hyponormality in single operators and spherically log-hyponormality in commuting pairs of operators.

Comments

Original published version available at https://doi.org/10.1080/03081087.2023.2236771

Recommended Citation

Won Kim, Hyung, Jaewoong Kim, and Jasang Yoon. "Spherical Aluthge transform, spherical p and log-hyponormality of commuting pairs of operators II." Linear and Multilinear Algebra 72, no. 13 (2024): 2134-2148. https://doi.org/10.1080/03081087.2023.2236771

Publication Title

Linear and Multilinear Algebra

DOI

10.1080/03081087.2023.2236771