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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Extrapolation spaces for $ C$-semigroups


Authors: Miao Li and Quan Zheng
Journal: Proc. Amer. Math. Soc. 137 (2009), 663-668
MSC (2000): Primary 47D06; Secondary 47D03
Published electronically: September 5, 2008
MathSciNet review: 2448588
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Abstract: Let $ \{T(t)\}_{t\geq 0}$ be a $ C$-semigroup on $ X$. We construct an extrapolation space $ X_s$, such that $ X$ can be continuously densely imbedded in $ X_s$, and $ \{T_s(t)\}_{t\geq 0}$, the extension of $ \{T(t)\}_{t\geq 0}$ to $ X_s$, is strongly uniformly continuous and contractive. Using this enlarged space, we give an answer to the question asked in [M. Li, F. L. Huang, Characterizations of contraction $ C$-semigroups, Proc. Amer. Math Soc. 126 (1998), 1063-1069] in the negative.


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Additional Information

Miao Li
Affiliation: Department of Mathematics, Sichuan University, Chengdu, Sichuan 610064, People’s Republic of China
Email: limiao1973@hotmail.com

Quan Zheng
Affiliation: Department of Mathematics, Huazhnog University of Science and Technology,Wuhan 430074, People’s Republic of China
Email: qzheng@hust.edu.cn

DOI: http://dx.doi.org/10.1090/S0002-9939-08-09556-7
PII: S 0002-9939(08)09556-7
Keywords: $C$-semigroups, contraction, $C_0$-semigroups, extrapolation space
Received by editor(s): October 16, 2006
Received by editor(s) in revised form: February 12, 2008
Published electronically: September 5, 2008
Additional Notes: The first author was supported by the NSF of China (Grant No. 10501032), and the second author by TRAPOYT and the NSF of China (Grant No. 10671079).
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2008 American Mathematical Society