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In this work, we define the set 
which consists of n-normal operators. Also, the sets 
and 
and defined from 
. Firstly, the set 
is proved Banach algebra and establish consists of n-normal operators. Secondly 
is shown C* -algebra, also some properties and theories are proved to reach a circular for the spectral theory. Finally, this study is established and proved generalization the spectral theory of n-normal operators.
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