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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Extrapolation spaces for $C$-semigroups
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by Miao Li and Quan Zheng PDF
Proc. Amer. Math. Soc. 137 (2009), 663-668 Request permission

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
  • 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
  • © Copyright 2008 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 137 (2009), 663-668
  • MSC (2000): Primary 47D06; Secondary 47D03
  • DOI: https://doi.org/10.1090/S0002-9939-08-09556-7
  • MathSciNet review: 2448588