Publications of the Research Institute for Mathematical Sciences


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Volume 34, Issue 6, 1998, pp. 579–590
DOI: 10.2977/prims/1195144424

Published online: 1998-12-31

Infinite Differentiability of Hermitian and Positive C-Semigroups and C-Cosine Functions

Yuan-Chuan Li[1] and Sen-Yen M. Shaw[2]

(1) National Central University, Chung-Li, Taiwan
(2) National Central University, Chung-Li, Taiwan

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, ∞).

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Li Yuan-Chuan, Shaw Sen-Yen: Infinite Differentiability of Hermitian and Positive C-Semigroups and C-Cosine Functions. Publ. Res. Inst. Math. Sci. 34 (1998), 579-590. doi: 10.2977/prims/1195144424