Author

L. Arnold

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Preprint Aug 2026

Positive strongly Kreiss bounded operators on $L^p$-spaces have logarithmic power growth

Let $1<p<\infty$ and let $T$ be a positive strongly Kreiss bounded operator on an $L^p$-space. We prove that there exist constants $C,\kappa>0$ such that \[ \|T^N\| \leq C \left( \log(N+1) \right)^\kappa, \qquad N \geq 1. \] This answers a question raised by Arnold and Cuny concerning positive strongly Kreiss bounded o...

L. Arnold · 0 citations

Preprint Aug 2026

Polynomial gaps below linear growth for Kreiss bounded semigroups and operators

We prove that every Kreiss bounded $C_0$-semigroup $(T_t)_{t\ge0}$ on a Hilbert space satisfies \[ \|T_t\|\le C(1+t)^{1-\varepsilon_K}, \qquad t\ge0, \] where $\varepsilon_K>0$ depends explicitly only on the Kreiss constant. The same conclusion is obtained for positive Kreiss bounded $C_0$-semigroups on $L^p$-spaces, $...

L. Arnold · 1 citation