L. Arnold

activity

20182026

most cited

S^{1}

-bounded Fourier multipliers on

H^{1} (R)

and functional calculus for semigroups

2 citations · 2 across the 14 of their papers we have counts for

collaborators

16 papers

math.FA2026

Self-improvement for absolutely Cesáro bounded operators

Loris Arnold

We prove that every $p$ -absolutely Cesàro bounded operator with constant $K > 1$ is $q$ -absolutely Cesàro bounded for $1 \leq q < p K / (K - 1)$ . This range is optimal, even for positive wei…

math.FA2026

On absolutely Cesàro bounded operators

Arafat Abbar, Loris Arnold, Clément Coine

We study $p$ -absolutely Cesàro bounded operators, with particular emphasis on self-improvement, weighted shifts, and linear dynamics. Our first main result shows that, for $1<p<\in…

math.FA2026

Uniform Kreiss boundedness does not imply strong Cesàro boundedness

Loris Arnold

We construct a uniformly Kreiss bounded operator on a separable Hilbert space which is not strongly Cesàro bounded. This gives a negative answer to a question of Cohen, Cuny, Eisne…

math.FA2026

Polynomial gaps below linear growth for Kreiss bounded semigroups and operators

Loris Arnold

We prove that every Kreiss bounded $C_{0}$ -semigroup $(T_{t})_{t \geq 0}$ on a Hilbert space satisfies \[ \|T_t\|\le C(1+t)^{1-\varepsilon_K}, \qquad t\ge0, \] where $ε_{K} > 0$ dep…

math.FA2026

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

Loris Arnold

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 $C, κ > 0$ such that \[ \|T^N\| \leq C \left( \log(N…

math.FA2026

Stability of Individually Eventually Positive Semigroups on $L^{p}$ -Spaces

Loris Arnold

We answer a question raised by Vogt by proving that the growth bound of an individually eventually positive $C_{0}$ -semigroup on an $L^{p}$ -space ( $1 < p < \infty$ ) coincides with the…

Self-improvement for absolutely Cesáro bounded operators

On absolutely Cesàro bounded operators

Uniform Kreiss boundedness does not imply strong Cesàro boundedness

Polynomial gaps below linear growth for Kreiss bounded semigroups and operators

Positive strongly Kreiss bounded operators on Lp-spaces have logarithmic power growth

Stability of Individually Eventually Positive Semigroups on Lp-Spaces

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

Stability of Individually Eventually Positive Semigroups on $L^{p}$ -Spaces