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Weak and Strong Approximation of Semigroups on Hilbert Spaces

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Abstract

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.

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Authors and Affiliations

  1. Institut für Analysis, Fakultät für Mathematik, TU Dresden, 01062, Dresden, Germany

    R. Chill

  2. Department of Mathematics, University of Auckland, Private Bag 92019, Auckland, 1142, New Zealand

    A. F. M. ter Elst

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  1. R. Chill
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  2. A. F. M. ter Elst
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Correspondence to R. Chill.

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Chill, R., ter Elst, A.F.M. Weak and Strong Approximation of Semigroups on Hilbert Spaces. Integr. Equ. Oper. Theory 90, 9 (2018). https://doi.org/10.1007/s00020-018-2439-5

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  • DOI: https://doi.org/10.1007/s00020-018-2439-5

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