Korean J. Math. Vol. 22 No. 2 (2014) pp.349-354
DOI: https://doi.org/10.11568/kjm.2014.22.2.349

Convergence of C0 semigroups in the weak topology

Article Sidebar

PDF
Published: Jun 24, 2014
Keywords:
contraction C0 semigroup, weak topology, convergence, equicontinuity, Lapalce transform
Mathematics Subject Classification:
47D06, 34K07

Main Article Content

Young Seop Lee
Department of Mathematics Seoul Women's University

Abstract

In this paper, we establish convergence of contraction C0 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].


Article Details

Supporting Agencies

This work was supported by a research grant from Seoul Women's University(2013).

References

[1] W. Arendt, C.J.K. Batty, M. Hieber and F. Neubrander Vector-Valued Laplace Transforms and Cauchy Problems, Monographs in Math. 96, Birkh ̈auser, 2001. Google Scholar

[2] T. Eisner, A. Ser eny, On the weak analogue of the Trotter-Kato theorem, Taiwanese J. Math. 14 (2010), 1411-1416. Google Scholar

[3] K. Engel, R. Nagel, One-Parameter Semigroups for linear evolution equations, Springer, Berlin, 2000. Google Scholar

[4] Y.S. Lee, Trotter-Kato Theorem in the weak topology, Korean J. Math. 21 (2013), 325–330. Google Scholar

[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. Google Scholar

[6] A. Pazy, Semigroups of linear operators and applications to partial differential equations, Springer-Verlag, 1983. Google Scholar

[7] T.J. Xiao and J. Liang Approximations of Laplace transforms and integrated semigroups, J. Funct. Anal. 172 (2000), 202-220. Google Scholar