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…

math.FA2026

Rates of Decay for $(α, β)$ -Ritt-Kreiss Operators

Loris Arnold

This paper investigates the growth of the sequences $(∥ T^{n} (I - T)^{k} ∥)_{n \geq 1}$ for bounded linear operators on Banach spaces under various resolvent conditions. Focusing on $α$ -Ri…

math.FA2023

On the growth rate of powers of a strongly Kreiss bounded operator on $L^{p}$ -spaces

Loris Arnold, Christophe Cuny

Let $T$ be a strongly Kreiss bounded linear operator on $L^{p}$ . We obtain a bound on the rate of growth of the norms of the powers of $T$ . The bound is optimal with respect to the p…

math.FA2023

Hankel operators on $L^{p} (R_{+})$ and their $p$ -completely bounded multipliers

Loris Arnold, Christian Le Merdy, Safoura Zadeh

We show that for any $1 < p < \infty$ , the space $H an k_{p} (R_{+}) \subseteq B (L^{p} (R_{+}))$ of all Hankel operators on $L^{p} (R_{+})$ is equal to the $w^{*}$ -closure of th…

math.FA2022

Growth rate of eventually positive Kreiss bounded $C_{0}$ -semigroups on $L^{p}$ and $C (K)$

L. Arnold, C. Coine

In this paper, we compare several Cesàro and Kreiss type boundedness conditions for a $C_{0}$ -semigroup on a Banach space and we show that those conditions are all equivalent for a p…

math.FA2022

Behavior of Kreiss bounded $C_{0}$ -semigroups on a Hilbert space

Loris Arnold

Let $0 < α \leq 1$ . We prove that a $α$ -Kreiss bounded $C_{0}$ semigroup $(T_{t})_{t \geq 0}$ on a Hilbert space has asymptotics $∣∣ T_{t} ∣∣ = O (t^{α} / l o g (t))$ . Then, we give an…

math.FA2022★ 2 cited

$S^{1}$ -bounded Fourier multipliers on $H^{1} (R)$ and functional calculus for semigroups

Loris Arnold, Christian Le Merdy, Safoura Zadeh

Let $T : H^{1} (R) \to H^{1} (R)$ be a bounded Fourier multiplier on the analytic Hardy space $H^{1} (R) \subset L^{1} (R)$ and let $m\in L^\infty({\m…

math.FA2020

Functional calculus for a bounded $C_{0}$ -semigroup on Hilbert space

Loris Arnold, Christian Le Merdy

We introduce a new Banach algebra $A (C_{+})$ of bounded analytic functions on $C_{+} = {z \in C : Re (z) > 0}$ which is an analytic versio…

math.FA2020

Derivative bounded functional calculus of power bounded operators on Banach spaces

Loris Arnold

In this article we study bounded operators $T$ on Banach space $X$ which satisfy the discrete Gomilko Shi-Feng condition $$\int_{0}^{2π}|\langle R(re^{it},T)^{2}x,x^*\rangle |dt \l…

math.FA2019

Gamma-boundedness of $C_{0}$ -semigroups and their $H^{\infty}$ -functional calculi

Loris Arnold

We discuss the notion of $γ$ - $H^{\infty}$ -bounded calculus, strong $γ$ - $m$ - $H^{\infty}$ -bounded calculus on half-plane and weak- $γ$ -Gomilko-Shi-Feng condition and give a connection…

math.FA2018

New counterexamples on Ritt operators, sectorial operators and R-boundedness

Loris Arnold, Christian Le Merdy

Let $D$ be a Schauder decomposition on some Banach space $X$ . We prove that if $D$ is not $R$ -Schauder, then there exists a Ritt operator $T \in B (X)$ which is a m…

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

Rates of Decay for (α,β)-Ritt-Kreiss Operators

On the growth rate of powers of a strongly Kreiss bounded operator on Lp-spaces

Hankel operators on Lp(R+​) and their p-completely bounded multipliers

Growth rate of eventually positive Kreiss bounded C0​-semigroups on Lp and C(K)

Behavior of Kreiss bounded C0​-semigroups on a Hilbert space

S1-bounded Fourier multipliers on H1(R) and functional calculus for semigroups

Functional calculus for a bounded C0​-semigroup on Hilbert space

Derivative bounded functional calculus of power bounded operators on Banach spaces

Gamma-boundedness of C0​-semigroups and their H∞-functional calculi

New counterexamples on Ritt operators, sectorial operators and R-boundedness

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

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

Rates of Decay for $(α, β)$ -Ritt-Kreiss Operators

On the growth rate of powers of a strongly Kreiss bounded operator on $L^{p}$ -spaces

Hankel operators on $L^{p} (R_{+})$ and their $p$ -completely bounded multipliers

Growth rate of eventually positive Kreiss bounded $C_{0}$ -semigroups on $L^{p}$ and $C (K)$

Behavior of Kreiss bounded $C_{0}$ -semigroups on a Hilbert space

$S^{1}$ -bounded Fourier multipliers on $H^{1} (R)$ and functional calculus for semigroups

Functional calculus for a bounded $C_{0}$ -semigroup on Hilbert space

Gamma-boundedness of $C_{0}$ -semigroups and their $H^{\infty}$ -functional calculi