Parahyponormality Modeling of Operator Inequality Dominatedby Norm Mapping

Abstract

In this article, new class of operators named -Parahyponormal operator is imposed. It is extended Paranormality, means it includes both paranormal and hyponormal operators. This concept is described analytically based on the Inequality Theory (IT). Furthermore, a new characteristic of -Parahyponormality is investigated and provided. Several analytical merits, such as adjoint, invertible, null set, power again, and scalar multiplication, are highlighted. Besides, some algebraic merits of this considered operator are discussed including addition, multiplication and tensor product. Some illustrative examples are also provided.