Jointly A-Paranormal Tuples of Operators in Semi-Hilbertian Spaces

This paper introduces the concept of jointly A-paranormal operator tuples acting on semi-Hilbertian spaces. We establish foundational operator inequalities and structural properties governing this new class. Specifically, we prove that joint A-paranormality is preserved under tensor products and stable under taking powers. Furthermore, we demonstrate that every commuting jointly A-hyponormal tuple is jointly A-paranormal. Since every commuting jointly A-paranormal tuple is jointly A-normaloid, we complete the hierarchy of multivariable operator classes within the semi-Hilbertian context.