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Triviality of the Peripheral Point Spectrum of Positive Semigroups on Atomic Banach Lattices

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Abstract

Generalizing a result of Keicher [4] we show that generators of positive C0-semigroups on super-atomic Banach lattices have trivial peripheral point spectrum provided they satisfy a certain growth condition.

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References

  1. E. B. Davies, Triviality of the peripheral point spectrum, J. Evol. Equ. (2005), 407–415.

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  4. V. Keicher, On the peripheral spectrum of bounded positive semigroups on atomic Banach lattices, Archiv d. Mathem., to appear.

  5. G. A. Lozanovskii, A. Mekler, Completely linear functionals and reflexivity in normed linear lattices, Izv. Vyss Ucebn. Zaved. Matematika, 66 (1967), 47–53.

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  7. H. H. Schaefer, Banach Lattices and Positive Operators, Springer, Berlin Heidelberg New York (1974).

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Correspondence to Manfred P. H. Wolff.

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Mathem. Institut d. Universität Tübingen in memoriam H. H. Schaefer

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Wolff, M.P.H. Triviality of the Peripheral Point Spectrum of Positive Semigroups on Atomic Banach Lattices. Positivity 12, 185–192 (2008). https://doi.org/10.1007/s11117-007-2151-1

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  • DOI: https://doi.org/10.1007/s11117-007-2151-1

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