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Characterizations of contraction $C$-semigroups


Authors: Miao Li and Falun Huang
Journal: Proc. Amer. Math. Soc. 126 (1998), 1063-1069
MSC (1991): Primary 47D03
DOI: https://doi.org/10.1090/S0002-9939-98-04243-9
MathSciNet review: 1443839
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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.


References [Enhancements On Off] (What's this?)

  • 1. E. B. Davies and M. M. Pang, The Cauchy problem and a generalization of the Hille-Yosida theorem, Proc. London Math. Soc. 55 (1987), 181-208. MR 88e:34100
  • 2. R. deLaubenfels, $C$-semigroups and the Cauchy problem, J. Funct. Anal. 111 (1993), 44-61. MR 94b:47055
  • 3. -, $C$-semigroups and strongly continuous semigroups, Israel J. Math. 81 (1993), 227-255. MR 95d:47047
  • 4. -, Existence families, functional calculi and evolution equations, Lecture Notes in Math., Vol. 1570, Springer Verlag, 1994. MR 96b:47047
  • 5. A. Pazy, Semigroups of linear operators and applications to partial differential equations, Springer-Verlag, New York, 1983. MR 85g:47061
  • 6. N. Tanaka, On the exponentially bounded $C$-semigroups, Tokyo J. Math. 10 (1987), 107-117. MR 88h:47063
  • 7. N. Tanaka and I. Miyadera, Exponentially bounded $C$-semigroups and integrated semigroups, Tokyo J. Math. 12 (1989), 99-115. MR 90g:47081
  • 8. -, Exponentially bounded $C$-semigroups and generation of semigroups, J. Math. Anal. Appl. 143 (1989), 358-378. MR 90k:47087
  • 9. Q. Zheng and Liping Liu, Almost periodic regularized groups, semigroups, and cosine functions, J. Math. Anal. Appl. 197 (1996), 90-162. MR 96m:47076

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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: https://doi.org/10.1090/S0002-9939-98-04243-9
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
Article copyright: © Copyright 1998 American Mathematical Society

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