Weak and Strong Approximation of Semigroups on Hilbert Spaces



For a sequence of uniformly bounded, degenerate semigroups on a Hilbert space, we compare various types of convergences to a limit semigroup. Among others, we show that convergence of the semigroups, or of the resolvents of the generators, in the weak operator topology, in the strong operator topology or in certain integral norms are equivalent under certain natural assumptions which are frequently met in applications.


Strong resolvent convergence Weak resolvent convergence Degenerate semigroup 

Mathematics Subject Classification

Primary 35B40 47D03 Secondary 47A05 65N30 


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Authors and Affiliations

  1. 1.Institut für Analysis, Fakultät für MathematikTU DresdenDresdenGermany
  2. 2.Department of MathematicsUniversity of AucklandAucklandNew Zealand

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