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TROTTER-KATO THEOREM IN THE WEAK TOPOLOGY

  • Received : 2013.07.31
  • Accepted : 2013.09.03
  • Published : 2013.09.30

Abstract

In this paper, we prove Trotter-Kato theorem in the weak topology if $X^*$ is a uniformly convex Banach space.

Keywords

References

  1. 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
  2. K. Engel, R. Nagel, One-Parameter Semigroups for linear evolution equations, Springer, Berlin, 2000
  3. 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
  4. I. Miyadera, Nonlinear Semigroups, Amer. Math. Soc., Providence, Rhode Island, 1992
  5. A. Pazy, Semigroups of linear operators and applications to partial differential equations, Springer-Verlag, 1983

Cited by

  1. A CONVERGENCE OF C0 SEMIGROUPS IN THE WEAK TOPOLOGY vol.22, pp.2, 2013, https://doi.org/10.11568/kjm.2014.22.2.349