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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Analyticity of positive semigroups is inherited under domination
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by Jochen Glück
Proc. Amer. Math. Soc. 151 (2023), 4793-4798
DOI: https://doi.org/10.1090/proc/16492
Published electronically: August 4, 2023

Abstract:

For positive $C_0$-semigroups $S$ and $T$ on a Banach lattice such that $S(t) \le T(t)$ for all times $t$, we prove that analyticity of $T$ implies analyticity of $S$. This answers an open problem posed by Arendt in 2004.

Our proof is based on a spectral theoretic argument: we apply spectral theory of positive operators to multiplication operators that are induced by $S$ and $T$ on a vector-valued function space.

References
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Bibliographic Information
  • Jochen Glück
  • Affiliation: University of Wuppertal, School of Mathematics and Natural Sciences, Gaußstr. 20, 42119 Wuppertal, Germany
  • ORCID: 0000-0002-0319-6913
  • Email: glueck@uni-wuppertal.de
  • Received by editor(s): May 2, 2022
  • Received by editor(s) in revised form: March 13, 2023, and March 25, 2023
  • Published electronically: August 4, 2023

  • Dedicated: Dedicated to the memory of Manfred P. H. Wolff
  • Communicated by: Adrian Ioana
  • © Copyright 2023 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 151 (2023), 4793-4798
  • MSC (2020): Primary 47D06, 47B65, 47A10
  • DOI: https://doi.org/10.1090/proc/16492
  • MathSciNet review: 4634882