Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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A CONVERGENCE OF C0 SEMIGROUPS IN THE WEAK TOPOLOGY

  • Received : 2014.04.23
  • Accepted : 2014.06.09
  • Published : 2014.06.30
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Abstract

In this paper, we establish convergence of contraction $C_0$ semigroups in the weak topology on a general Banach space. We remove the restriction on a Banach space X and weaken the condition on resolvents of generators in the previous results [4, 5].

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References

  1. W. Arendt, C.J.K. Batty, M. Hieber and F. Neubrander Vector-Valued Laplace Transforms and Cauchy Problems, Monographs in Math. 96, Birkhauser, 2001.
  2. T. Eisner, A. Sereny, On the weak analogue of the Trotter-Kato theorem, Taiwanese J. Math. 14 (2010), 1411-1416. https://doi.org/10.11650/twjm/1500405956
  3. K. Engel, R. Nagel, One-Parameter Semigroups for linear evolution equations, Springer, Berlin, 2000.
  4. Y.S. Lee, Trotter-Kato Theorem in the weak topology, Korean J. Math. 21 (2013), 325-330. https://doi.org/10.11568/kjm.2013.21.3.325
  5. G. Marinoschi, A Trotter-Kato Theorem in the weak topology and an application to a singular perturbed problem, J. Math. Anal. Appl. 386 (2012), 50-60. https://doi.org/10.1016/j.jmaa.2011.07.039
  6. A. Pazy, Semigroups of linear operators and applications to partial differential equations, Springer-Verlag, 1983.
  7. T.J. Xiao and J. Liang Approximations of Laplace transforms and integrated semigroups, J. Funct. Anal. 172 (2000), 202-220. https://doi.org/10.1006/jfan.1999.3545