P. Leonetti

collaborators

5 papers

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,…

math.FA2019

Characterizations of the Ideal Core

Paolo Leonetti

Given an ideal $I$ on $ω$ and a sequence $x$ in a topological vector space, we let the $I$ -core of $x$ be the least closed convex set containing $\{x_n: n \noti…

math.FA2017

Duality between Measure and Category of Almost All Subsequences of a Given Sequence

Paolo Leonetti, Harry Miller, Leila Miller-Van Wieren

Let $S$ be the set of subsequences $(x_{n_{k}})$ of a given real sequence $(x_{n})$ which preserve the set of statistical cluster points. It has been recently shown that $S$ is a set o…

math.FA2017

On the Relationship between Ideal Cluster Points and Ideal Limit Points

Marek Balcerzak, Paolo Leonetti

Let $X$ be a first countable space which admits a non-trivial convergent sequence and let $I$ be an analytic P-ideal. First, it is shown that the sets of $I$ -li…

math.CA2017

A Characterization of Convex Functions

Paolo Leonetti

Let $D$ be a convex subset of a real vector space. It is shown that a radially lower semicontinuous function $f : D \to R \cup {+ \infty}$ is convex if and only if for all $…