Affiliation:
1. Facultad de Ciencias Fisico Matemáticas Benemérita Universidad Autónoma de Puebla Puebla Mexico
2. Department of Mathematics Korea Military Academy Seoul South Korea
3. School of Mathematical and Statistical Sciences The University of Texas Rio Grande Valley Edinburg Texas USA
Abstract
AbstractIn this paper, we introduce the notion of generalized spherical Aluthge transforms for commuting pairs of operators and study nontrivial joint invariant (resp. hyperinvariant) subspaces between the generalized spherical Aluthge transform and the original commuting pair. Next, we study the norm continuity through generalized Aluthge transform maps. We also study how the Taylor spectra and the Fredrolm index of commuting pairs of operators behave under the spherical Duggal transform. Finally, we introduce the notion of Campbell binormality for commuting pairs of operators and investigate some of its basic properties under spherical Aluthge and Duggal transforms. Moreover, we obtain new set inclusion diagrams among normal, quasinormal, centered, and Campbell binormal commuting pairs of operators.
Funder
National Research Foundation of Korea
University of Texas System