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Characterizations of contraction $C$-semigroups

Author(s): Miao Li; Falun Huang
Journal: Proc. Amer. Math. Soc. 126 (1998), 1063-1069.
MSC (1991): Primary 47D03
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Abstract: A $C$-semigroup $\{T(t)\}_{t\ge 0}$ is of contractions if $\|T(t)x\|\le \|Cx\|$ for $t\ge 0$, $x\in X$. Using the Hille-Yosida space, we completely characterize the generators of contraction $C$-semigroups. We also give the Lumer-Phillips theorem for $C$-semigroups in several special cases.

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Additional Information:

Miao Li
Affiliation: Department of Mathematics, Sichuan Union University, Chengdu 610064, People's Republic of China

Falun Huang
Affiliation: Department of Mathematics, Sichuan Union University, Chengdu 610064, People's Republic of China

DOI: 10.1090/S0002-9939-98-04243-9
PII: S 0002-9939(98)04243-9
Keywords: $C$-semigroups, $C_0$-semigroups, contraction, dissipative
Received by editor(s): June 13, 1996
Received by editor(s) in revised form: September 23, 1996
Additional Notes: This project was supported by the National Science Foundation of China
Communicated by: Palle E. T. Jorgensen
Copyright of article: Copyright 1998, American Mathematical Society

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