Kyoto Journal of Mathematics

Semigroups preserving a convex set in a Banach space

Ichiro Shigekawa

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We discuss semigroups that preserve a convex set in a Banach space or a Hilbert space. We give sufficient conditions for which a semigroup preserves a convex set. Using this, we show that various issues can be treated in a unified way. We also discuss the problem in the Hilbert space setting, in which we use the sesquilinear form associated with a semigroup.

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Kyoto J. Math., Volume 51, Number 3 (2011), 647-672.

First available in Project Euclid: 1 August 2011

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Primary: 47D06: One-parameter semigroups and linear evolution equations [See also 34G10, 34K30] 47D07: Markov semigroups and applications to diffusion processes {For Markov processes, see 60Jxx} 60J45: Probabilistic potential theory [See also 31Cxx, 31D05]


Shigekawa, Ichiro. Semigroups preserving a convex set in a Banach space. Kyoto J. Math. 51 (2011), no. 3, 647--672. doi:10.1215/21562261-1299918.

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