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, ∞); (2) hermitian C-cosine functions are norm continuous at either non or all of points in [0, ∞); (3) positive C-semigroups which dominate C are infinitely differentiable in opetator norm on [0, ∞); (4) positive C-cosine functions are infinitely differentiable in operator norm on [0, ∞).
Cite this article
Yuan-Chuan Li, Sen-Yen M. Shaw, Infinite Differentiability of Hermitian and Positive <i>C</i>-Semigroups and <i>C</i>-Cosine Functions. Publ. Res. Inst. Math. Sci. 34 (1998), no. 6, pp. 579–590