P. Leonetti

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20172022

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10 papers · 1 filter

math.FA2022

On some locally convex FK spaces

Paolo Leonetti, Cihan Orhan

We provide necessary and/or sufficient conditions on vector spaces $V$ of real sequences to be a Fréchet space such that each coordinate map is continuous, that is, to be a locally…

math.FA2022

A Characterization of the Vector Lattice of Measurable Functions

Simone Cerreia-Vioglio, Paolo Leonetti, Fabio Maccheroni

Given a probability measure space $(X, Σ, μ)$ , it is well known that the Riesz space $L^{0} (μ)$ of equivalence classes of measurable functions $f : X \to R$ is universally comp…

math.FA2020

Tauberian theorems for ordinary convergence

Paolo Leonetti

We show that a real sequence $x$ is convergent if and only if there exist a regular matrix $A$ and an $F_{σ δ}$ -ideal $I$ on $N$ such that the set of subsequences…

math.FA2020

Turnpike in infinite dimension

Paolo Leonetti, Michele Caprio

Let $Φ$ be a correspondence from a normed vector space $X$ into itself, let $u : X \to R$ be a function, and $I$ be an ideal on $N$ . Also, assume that the…

math.FA2019

A Tauberian theorem for ideal statistical convergence

Marek Balcerzak, Paolo Leonetti

Given an ideal $I$ on the positive integers, a real sequence $(x_{n})$ is said to be $I$ -statistically convergent to $ℓ$ provided that $$ \textstyle \left\{n \…

math.FA2019

The general linear equation on open connected sets

Paolo Leonetti, Jens Schwaiger

Fix non-zero reals $α_{1}, \dots, α_{n}$ with $n \geq 2$ and let $K$ be a non-empty open connected set in a topological vector space such that $\sum_{i \leq n} α_{i} K \subseteq K$ (which holds,…