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

Convergence of $C_0$ semigroups in the weak topology

Young Seop Lee

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].

Keywords


contraction $C_{0}$ semigroup, weak topology, convergence, equicontinuity, Lapalce transform

Subject classification

47D06, 34K07

Sponsor(s)

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

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References


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