Spectral and Asymptotic Properties of Contractive Semigroups on Non-Hilbert Spaces release_ennfsrug3ngddnattmzuffzinq

by Jochen Glück

Released as a article .

2016  

Abstract

We analyse C_0-semigroups of contractive operators on real-valued L^p-spaces for p = 2 and on other classes of non-Hilbert spaces. We show that, under some regularity assumptions on the semigroup, the geometry of the unit ball of those spaces forces the semigroup's generator to have only trivial (point) spectrum on the imaginary axis. This has interesting consequences for the asymptotic behaviour as t →∞. For example, we can show that a contractive and eventually norm continuous C_0-semigroup on a real-valued L^p-space automatically converges strongly if p ∈{1,2,∞}.
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Date   2016-02-27
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arXiv  1410.2502v2
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