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 .
