Paolo Leonetti
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Previous Organizations / Institutes
The organizations / institutes from the scholar's other articles in the past ten years
Paolo Leonetti has a total of 41 co-authors. Here are the top co-authors by number of shared publications:
- Salvatore Tringali
School of Mathematical Sciences Hebei Normal University Shijiazhuang Hebei Province China
12 shared publications - Marek Balcerzak
Institute of Mathematics, Lodz University of Technology, Lodz, Poland
8 shared publications - Carlo Sanna
Department of Mathematical Sciences, Polytechnic of Turin, Turin, Italy
6 shared publications - Fabio Maccheroni
Bocconi University
6 shared publications - Salvatore Tringali
Texas A&M Univ Qatar, Dept Math, POB 23874, Doha, Qatar
6 shared publications - Dorota Głazowska
Institute of Mathematics, University of Zielona Góra, Zielona Góra, Poland
4 shared publications
Latest Publications
- Open Access
- 13 October 2026
- Published by Elsevier in Journal of Mathematical Analysis and Applications
- Vol. 568 (1)
Completeness and additive property for submeasures
- 13 October 2026
- Published by Elsevier in Journal of Mathematical Analysis and Applications
- Vol. 568 (1)
Open AccessCompleteness and additive property for submeasures
- Open Access
- 6 October 2026
- Published by Elsevier in Journal of Mathematical Analysis and Applications
- Vol. 567 (2)
Linear relations modulo meager sets
- 6 October 2026
- Published by Elsevier in Journal of Mathematical Analysis and Applications
- Vol. 567 (2)
Open AccessLinear relations modulo meager sets
- Open Access
On rough ideal convergence
We continue the study of ideal convergence for sequences $(x_n)$ with values in a topological space $X$ with respect to a family $\{F_η:η\in X\}$ of subsets of $X$ with $η\in F_η$, where each $F_η$ measures the allowed ``roughness'' of convergence toward $η$. More precisely, after introducing the corresponding notions of cluster and limit points, we prove several inclusion and invariance properties, discuss their structural properties, and give examples showing that the rough notions are genuinely different from the classical ideal ones.Open AccessOn rough ideal convergence
We continue the study of ideal convergence for sequences $(x_n)$ with values in a topological space $X$ with respect to a family $\{F_η:η\in X\}$ of subsets of $X$ with $η\in F_η$, where each $F_η$ measures the allowed ``roughness'' of convergence toward $η$. More precisely, after introducing the corresponding notions of cluster and limit points, we prove several inclusion and invariance properties, discuss their structural properties, and give examples showing that the rough notions are genuinely different from the classical ideal ones. - Open Access
Sets of Ramsey-limit points and IP-limit points
Let $X$ be an uncountable Polish space and let $\mathcal{H}$ be the Hindman ideal, that is, the family of all $S\subseteq ω$ which are not $IP$-sets. For each sequence $x=(x_n)_{n \in ω}$ taking values in $X$, let $Λ_{x}(FS)$ be the set of $IP$-limit points of $x$. Also, let $Λ_{x}(\mathcal{H})$ be the set of $\mathcal{H}$-limit points of $x$, that is, the set of ordinary limits of subsequences $(x_n)_{n \in S}$ with $S\notin \mathcal{H}$. After proving that these two notions do not coincide in general, we show that both families of nonempty sets of the type $Λ_{x}(FS)$ and of the type $Λ_{x}(\mathcal{H})$ are precisely the class of nonempty analytic subsets of $X$. An analogous result holds also for Ramsey convergence. In the proofs, we use the concept of partition regular functions introduced in J. Symb. Log. (2024) [doi:10.1017/jsl.2024.8], which provide a unified approach to these types of convergence.Open AccessSets of Ramsey-limit points and IP-limit points
Let $X$ be an uncountable Polish space and let $\mathcal{H}$ be the Hindman ideal, that is, the family of all $S\subseteq ω$ which are not $IP$-sets. For each sequence $x=(x_n)_{n \in ω}$ taking values in $X$, let $Λ_{x}(FS)$ be the set of $IP$-limit points of $x$. Also, let $Λ_{x}(\mathcal{H})$ be the set of $\mathcal{H}$-limit points of $x$, that is, the set of ordinary limits of subsequences $(x_n)_{n \in S}$ with $S\notin \mathcal{H}$. After proving that these two notions do not coincide in general, we show that both families of nonempty sets of the type $Λ_{x}(FS)$ and of the type $Λ_{x}(\mathcal{H})$ are precisely the class of nonempty analytic subsets of $X$. An analogous result holds also for Ramsey convergence. In the proofs, we use the concept of partition regular functions introduced in J. Symb. Log. (2024) [doi:10.1017/jsl.2024.8], which provide a unified approach to these types of convergence. - 14 January 2026
- Published by American Mathematical Society (AMS) in Proceedings of the American Mathematical Society
- Vol. 154 (3) , 1153-1166
On uniform summability
Let A \mathscr {A} be a nonempty set of infinite matrices of linear operators between two topological vector spaces. We show that a sequence is uniformly A \mathscr {A} -summable if and only if it is B B -summable for all matrices B B of linear operators such that the n n th row of B B is the n n th row for some A ∈ A A \in \mathscr {A} . This extends the main result of Bell in [Proc. Amer. Math. Soc. 38 (1973), pp. 548–552]. We also provide several applications including uniform versions of Silverman–Toeplitz theorem, characterizations of almost regular matrices, uniform superior limits, and inclusion of ideal cores. Basically, our methods allow to translate ordinary results into their uniform versions, using directly the former ones.
- 14 January 2026
- Published by American Mathematical Society (AMS) in Proceedings of the American Mathematical Society
- Vol. 154 (3) , 1153-1166
On uniform summability
Let A \mathscr {A} be a nonempty set of infinite matrices of linear operators between two topological vector spaces. We show that a sequence is uniformly A \mathscr {A} -summable if and only if it is B B -summable for all matrices B B of linear operators such that the n n th row of B B is the n n th row for some A ∈ A A \in \mathscr {A} . This extends the main result of Bell in [Proc. Amer. Math. Soc. 38 (1973), pp. 548–552]. We also provide several applications including uniform versions of Silverman–Toeplitz theorem, characterizations of almost regular matrices, uniform superior limits, and inclusion of ideal cores. Basically, our methods allow to translate ordinary results into their uniform versions, using directly the former ones.
- 10 October 2025
- Published by Springer Nature in Results in Mathematics
- Vol. 80 (8) , 1-13
On the Ingham–Jessen Inequality for Measure Spaces
- 10 October 2025
- Published by Springer Nature in Results in Mathematics
- Vol. 80 (8) , 1-13
On the Ingham–Jessen Inequality for Measure Spaces
- Open Access
- 25 September 2025
- Published by Elsevier in Journal of Mathematical Analysis and Applications
- Vol. 556 (1)
On generalized limits and ultrafilters
- 25 September 2025
- Published by Elsevier in Journal of Mathematical Analysis and Applications
- Vol. 556 (1)
Open AccessOn generalized limits and ultrafilters
- Open Access
Can a small Gaussian perturbation break subadditivity?
Given an integer $a\ge 1$, a function $f: \mathbb{R}\to \mathbb{R}$ is said to be $a$-subadditive if $$ f(ax+y) \le af(x)+f(y) \,\,\,\text{ for all }x,y \in \mathbb{R}. $$ Of course, $1$-subadditive functions (which correspond to ordinary subadditive functions) are $2$-subadditive. % and $3$-subadditive. Answering a question of Matkowski, we show that there exists a continuous function $f$ satisfying $f(0)=0$ which is $2$-subadditive but not $1$-subadditive. In addition, the same example is not $3$-subadditive, which shows that the sequence of families of continuous $a$-subadditive functions passing through the origin is not increasing with respect to $a$. The construction relies on a perturbation of a given subadditive function with an even Gaussian ring, which will destroy the original subadditivity while keeping the weaker property. Lastly, given a positive rational cone $H\subseteq (0,\infty)$ which is not finitely generated, we prove that there exists a subadditive bijection $f:H\to H$ such that $\liminf_{x\to 0}f(x)=0$ and $\limsup_{x\to 0}f(x)=1$. This is related an open question of Matkowski and {Ś}wi{\k a}tkowski in [Proc. Amer. Math. Soc. 119 (1993), 187--197].Open AccessCan a small Gaussian perturbation break subadditivity?
Given an integer $a\ge 1$, a function $f: \mathbb{R}\to \mathbb{R}$ is said to be $a$-subadditive if $$ f(ax+y) \le af(x)+f(y) \,\,\,\text{ for all }x,y \in \mathbb{R}. $$ Of course, $1$-subadditive functions (which correspond to ordinary subadditive functions) are $2$-subadditive. % and $3$-subadditive. Answering a question of Matkowski, we show that there exists a continuous function $f$ satisfying $f(0)=0$ which is $2$-subadditive but not $1$-subadditive. In addition, the same example is not $3$-subadditive, which shows that the sequence of families of continuous $a$-subadditive functions passing through the origin is not increasing with respect to $a$. The construction relies on a perturbation of a given subadditive function with an even Gaussian ring, which will destroy the original subadditivity while keeping the weaker property. Lastly, given a positive rational cone $H\subseteq (0,\infty)$ which is not finitely generated, we prove that there exists a subadditive bijection $f:H\to H$ such that $\liminf_{x\to 0}f(x)=0$ and $\limsup_{x\to 0}f(x)=1$. This is related an open question of Matkowski and {Ś}wi{\k a}tkowski in [Proc. Amer. Math. Soc. 119 (1993), 187--197]. - Open Access
On the complexity of upper frequently hypercyclic vectors
Given a continuous linear operator $T:X\to X$, where $X$ is a topological vector space, let $\mathrm{UFHC}(T)$ be the set of upper frequently hypercyclic vectors, that is, the set of vectors $x \in X$ such that $\{n \in ω: T^nx \in U\}$ has positive upper asymptotic density for all nonempty open sets $U\subseteq X$. It is known that $\mathrm{UFHC}(T)$ is a $G_{δσδ}$-set which is either empty or contains a dense $G_δ$-set. Using a purely topological proof, we improve it by showing that $\mathrm{UFHC}(T)$ is always a $G_{δσ}$-set. Bonilla and Grosse-Erdmann asked in [Rev. Mat. Complut. \textbf{31} (2018), 673--711] whether $\mathrm{UFHC}(T)$ is always a $G_δ$-set. We answer such question in the negative, by showing that there exists a continuous linear operator $T$ for which $\mathrm{UFHC}(T)$ is not a $F_{σδ}$-set (hence not $G_δ$). In addition, we study the [non-]equivalence between (the ideal versions of) upper frequently hypercyclicity in the product topology and upper frequently hypercyclicity in the norm topology.Open AccessOn the complexity of upper frequently hypercyclic vectors
Given a continuous linear operator $T:X\to X$, where $X$ is a topological vector space, let $\mathrm{UFHC}(T)$ be the set of upper frequently hypercyclic vectors, that is, the set of vectors $x \in X$ such that $\{n \in ω: T^nx \in U\}$ has positive upper asymptotic density for all nonempty open sets $U\subseteq X$. It is known that $\mathrm{UFHC}(T)$ is a $G_{δσδ}$-set which is either empty or contains a dense $G_δ$-set. Using a purely topological proof, we improve it by showing that $\mathrm{UFHC}(T)$ is always a $G_{δσ}$-set. Bonilla and Grosse-Erdmann asked in [Rev. Mat. Complut. \textbf{31} (2018), 673--711] whether $\mathrm{UFHC}(T)$ is always a $G_δ$-set. We answer such question in the negative, by showing that there exists a continuous linear operator $T$ for which $\mathrm{UFHC}(T)$ is not a $F_{σδ}$-set (hence not $G_δ$). In addition, we study the [non-]equivalence between (the ideal versions of) upper frequently hypercyclicity in the product topology and upper frequently hypercyclicity in the norm topology.