L. Arnold

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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 $(I^\pm, I^^{2})$ -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 $I^\pm$ -R…

math.FA2026

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.FA2025

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.FA2025

$S^{1}$ -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.FA2025

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…

Stability of Individually Eventually Positive Semigroups on Lp-Spaces

Rates of Decay for (I^±,I^2)-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

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

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

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

Rates of Decay for $(I^\pm, I^^{2})$ -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

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

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