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Norm inequalities for holomorphic semigroups

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Abstract

Let (a z)Rez>0 be a holomorphic semigroup in a Banach algebra. Provided that a certain integral along the line Rez=1 is finite, it is possible to estimate ‖a z‖ purely in terms of this integral and the spectral radius ofa. This generalizes earlier results of Esterle and Sinclair (used to prove tauberian theorems), which were applicable just to radical Banach algebras.

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References

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Authors and Affiliations

  1. Département de mathématiques et de statistique, Université Laval, G1K 7P4, Québec, QC, Canada

    T. J. Ransford

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  1. T. J. Ransford
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Correspondence to T. J. Ransford.

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Research supported by grants from the Natural Science and Engineering Research Council of Canada and the Fonds FCAR of the Province of Québec.

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Ransford, T.J. Norm inequalities for holomorphic semigroups. Isr. J. Math. 97, 157–173 (1997). https://doi.org/10.1007/BF02774033

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  • DOI: https://doi.org/10.1007/BF02774033

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