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Spectral properties of operator logarithms

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Abstract.

We prove that the spectral height of the logarithm log A of a sectorial operator A equals the spectral angle of A. This yields old results of Prüss/Sohr and McIntosh as corollaries. Then we construct a sectorial operator A on a UMD space having bounded imaginary powers such that the group type of (A is) s ∈ℝ is strictly greater than π.

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  1. Abt. Angewandte Analysis, Universität Ulm, Helmholtzstraße 18, 89069, Ulm

    Markus Haase

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  1. Markus Haase
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Correspondence to Markus Haase.

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Mathematics Subject Classification (2000):47A60,47D06.

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Haase, M. Spectral properties of operator logarithms. Math. Z. 245, 761–779 (2003). https://doi.org/10.1007/s00209-003-0569-0

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  • DOI: https://doi.org/10.1007/s00209-003-0569-0

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