Results of Hankel Semigroup of Linear Operator as Eventually Uniform Continuous Semigroup

This paper consists of Hankel results of ω -order reversing partial contraction as a semigroup of linear operator. Spectral mapping theorem was investigated and it was established that ω -order reversing partial contraction mapping is an eventually uniform continuous semigroup in which we showed that the proof of the extension of T ( t ) to a C 0 -semigroup ̂ T ( t ) on a space ̂ X containing X isometrically bounded. The space is constructed in such a way that the spectrum of the generator A of T ( t ) coincides with the spectrum of the generator  of ̂ T ( t ) and the approximate point spectrum of A coincides with the point spectrum of  .