A Spectral Bound for Asymptotically Norm-continuous Semigroups

  title={A Spectral Bound for Asymptotically Norm-continuous Semigroups},
  author={Mark D. Blake},
We introduce a new growth bound for C 0-semigroups giving information about the absence of norm-continuity of the semigroup and we give a corresponding spectral bound. For semigroups on general Ba-nach spaces we prove an inequality between these bounds and we give a version of the spectral mapping theorem in terms of the new growth bound. For semigroups on Hilbert space we show that the bounds are equal and hence obtain new characterizations of asymptotically norm-continuous semigroups and… CONTINUE READING

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