About C0 semigroup

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Let X is Banach space. Let T(t) is a semigroup on X.(t≧0)If there exists M≧1,ω≧0, will T(t) become a C0 semigroup? I know the converse holds true, but I'm not sure about this proposition. I would be glad to have a proof if it is valid, and a counterexample if it is not.