The mechanism of managing religious difference

God is the Lord of the worlds, forget them and their jinn, Arabs and non-Muslims, He is the Lord of Muslims and Lord of non-Muslims, as He created them male and female despite their differences in tongues and colors, so He created them according to their diversity and distinction in beliefs and religions.

 To prevent flare-ups due to differences, the Lord of the worlds set limits that he has forbidden to cross, and draw clear maps as mechanisms for managing religious differences and lifting psychological barriers between the different, so that they can coexist in peace and freedom, each adhering to his faith, and practicing the rituals of his religion.

We study in this paper the composition operator of induced by the function ?(z)=sz+t where , and We characterize the normal composition operator C? on Hardy space H2 and other related classes of operators. In addition to that we study the essential normality of C? and give some other partial results which are new to the best of our knowledge.

Through this study, the following has been proven, if  is an algebraically paranormal operator acting on separable Hilbert space, then  satisfies the ( ) property and  is also satisfies the ( ) property for all . These results are also achieved for  ( ) property.    In addition, we prove that for a polaroid operator with finite ascent then after the property ( ) holds for  for all.

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