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Relatively Bounded Rank One Perturbations of Non-Analytic Semigroups Can Generate Large Point Spectrum

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Abstract

It is known that relatively bounded compact perturbations of analytic semigroups yield again generators of analytic semigroups. On the other hand, for each non-analytic semigroup there is a relatively bounded rank one perturbation which is no longer a generator. In this note we show that in fact any non-analytic semigroup admits a relatively bounded rank one perturbation with a sequence of eigenvalues zj such that the real parts R(zj) converge to infinity.

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Authors and Affiliations

  1. Department of Mathematics, Ivan Franko Lviv National University, Universytetska 1, Lviv 79000, Ukraine

    Wolfgang Desch, Gudrun Schappacher & Wilhelm Schappacher

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  1. Wolfgang Desch
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  2. Gudrun Schappacher
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  3. Wilhelm Schappacher
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Correspondence to Wolfgang Desch, Gudrun Schappacher or Wilhelm Schappacher.

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Desch, W., Schappacher, G. & Schappacher, W. Relatively Bounded Rank One Perturbations of Non-Analytic Semigroups Can Generate Large Point Spectrum. Semigroup Forum 75, 470–476 (2007). https://doi.org/10.1007/s00233-007-0716-8

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  • DOI: https://doi.org/10.1007/s00233-007-0716-8

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