ON SKEW QUASI-P-CLASS (Q) OPERATORS, POSIMETRICALLY EQUIVALENT OPERATORS, AND MUTUALLY CLASS (Q) OPERATORS

Abstract

The study of class (Q) operators on Hilbert spaces has been exploited into various classes such as Quasi class (Q) , M-Quasi class (Q) , (n+k)-Class (Q) , Almost class (Q) and (α, β)- class (Q) among others . Results have been proved showing that some of these classes converge to the strong operator topology and results striking relationships between these classes and other general classes were achieved . However , little has been done to expand the results of class (Q) operators into the class of skew-Quasi-p-class (Q) . Hence, in this study, we introduce the category of Skew Quasi-p-class (Q) operators. We examine the fundamental characteristics of this class and establish its connection with other classes, such as quasi-p-normal operators . We also introduce the class of Posimetrically equivalent operators which is a generalization of Metrically equivalent operators , we characterize this class in terms of Complex symmetric operators and study their relations with other equivalence relations such as the class of n Metrically equivalent operators . We finally introduce the class of Mutually class (Q) operators . Furthermore, we explore the interrelation between this class and other classes in a comprehensive manner . The methodology used include but not limited to , properties of operators like unitary operators , quasi-p-normal operators and skew-adjoint operators . Results shows that the class of skew quasi-p-class (Q) operators have Bishop’s property and that they are isoloid and polaroid ; Posimetrically equivalent operators are closed under scalar multiplication and Mutually class (Q) operators are related to class (Q) operators . The study of these classes of (Q) operators will be helpful in the telecommunication industry by generalizing the allocation of network resources basing on priority of network . As a result , high-priority traffic such as video and voice will be given more bandwidth by being transmitted with lower packet loss and delay .