Intermediate and extrapolated spaces for bi-continuous operator semigroups

Abstract

We discuss the construction of the entire Sobolev (Hölder) scale for non-densely defined operators with rays of minimal growth on a Banach space. In particular, we give a construction for extrapolation- and Favard spaces of generators of (bi-continuous) semigroups, or which is essentially the same, Hille–Yosida operators on Saks spaces.

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Acknowledgements

We are indebted to Rainer Nagel and Sven-Ake Wegner for motivating discussions.

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Correspondence to Bálint Farkas.

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Budde, C., Farkas, B. Intermediate and extrapolated spaces for bi-continuous operator semigroups. J. Evol. Equ. 19, 321–359 (2019). https://doi.org/10.1007/s00028-018-0477-8

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Mathematics Subject Classification

  • 47D03
  • 46A70

Keywords

  • Extrapolation spaces
  • Non-densely defined Hille–Yosida operators
  • Not strongly continuous one-parameter operator semigroups
  • Saks spaces
  • Bi-continuous semigroups