J. Korean Math. Soc. 2016; 53(4): 895-908
Printed July 1, 2016
https://doi.org/10.4134/JKMS.j150334
Copyright © The Korean Mathematical Society.
Dohan Kim, Rinko Miyazaki, Toshiki Naito, and Jong Son Shin
Seoul National University, Shizuoka University, The University of Electro-Communications, Hosei University
Firstly, we establish spectral mapping theorems for normal eigenvalues (due to Browder) of a $C_0$-semigroup and its generator. Secondly, we discuss relationships between normal eigenvalues of the compact monodromy operator and the generator of the evolution semigroup on $P_{\tau}(X)$ associated with the $\tau$-periodic evolutionary process on a Banach space $X$, where $P_{\tau}(X)$ stands for the space of all $\tau$-periodic continuous functions mapping ${\mathbb R}$ to $X$.
Keywords: $C_0$-semigroup, evolution semigroup, monodromy operator, normal eigenvalue, order of pole, ascent
MSC numbers: Primary 47A10, 47D06; Secondary 35K05
2020; 57(1): 61-88
2017; 54(6): 1853-1878
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