On p-hyponormal operators on quaternionic Hilbert spaces

Abstract: This paper extends the notion of a p-hyponormal operator for a bounded right linear quaternionic operator defined on a right quaternionic Hilbert space. Several fundamental properties of complex p-hyponormal operators are investigated for the quaternionic ones. To develop the results, we prove the well-known Furuta inequality for quaternionic positive operators. This inequality opens the way to discuss the p-hyponormality of a quaternionic operator and its Aluthge transform. Finally, a new class of quaternionic operators is established between quaternionic p-hyponormal and quaternionic paranormal operators.