Let C be a bounded linear operator which is not necessarily injective. The following statements are proved: (1) hermitian C-semigroups are infinitely differentiable in operator norm on (0, infinity); (2) hermitian C-cosine functions are norm continuous at either non or all of points in [0, infinity); (3) positive C-semigroups which dominate C are infinitely differentiable in opetator norm on [0, infinity); (4) positive C-cosine functions are infinitely differentiable in operator norm on [0, infinity).
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