arXiv subjects

Victor dos Santos Ronchim

Publications and source records attributed to Victor dos Santos Ronchim.

4 recordsLinked to original sources

arXiv2025

Isometries of James-Schreier and Lorentz spaces

We study the group of surjective linear isometries on certain real Banach sequence spaces using the preservation of extreme points in the closed unit ball. Our main result provides a characterization of the extreme points of the dual unit ball of the James-Schreier space $V_1$. As a consequence, we show that the only isometries on $V_1$ are $\pm Id$. We also obtain a Banach-Stone-type result for Lorentz sequence spaces, analogous to one proved in \cite{CarothersIsometrisLorentz} for Lorentz function spaces.

math.FA↗

arXiv2022

Extension of $c_0(I)$-valued operators on spaces of continuous functions on compact lines

We investigate the problem of existence of a bounded extension to $C(K)$ of a bounded $c_0(I)$-valued operator $T$ defined on the subalgebra of $C(K)$ induced by a continuous increasing surjection $ϕ:K\to L$, where $K$ and $L$ are compact lines. Generalizations of some of the results of [6] about extension of $c_0$-valued operators are obtained. For instance, we prove that when a bounded extension of $T$ exists then an extension can be obtained with norm at most twice the norm of $T$. Moreover, the class of compact lines $L$ for which the $c_0$-extension property is equivalent to the $c_0(I)$-extension property for any continuous increasing surjection $ϕ:K\to L$ is studied.

math.FA↗

arXiv2021

Special sets of reals and weak forms of normality on Isbell-Mrówka spaces

We recall some classical results relating normality and some natural weakenings of normality in $Ψ$-spaces over almost disjoint families of branches in the Cantor tree to special sets of reals like $Q$-sets, $λ$-sets and $σ$-sets. We introduce a new class of special sets of reals which corresponds the corresponding almost disjoint family of branches being $\aleph_0$-separated. This new class fits between $λ$-sets and perfectly meager sets. We also discuss conditions for an almost disjoint family $\mathcal A$ being potentially almost-normal (pseudonormal), in the sense that $\mathcal A$ is almost-normal (pseudonormal) in some c.c.c. forcing extension.

math.GN↗

arXiv2020

Almost-normality of Isbell-Mrówka spaces

We explore almost-normality in Isbell-Mrówka spaces and some related concepts. We use forcing to provide an example of an almost-normal not normal almost disjoint family, explore the concept of semi-normality in Isbell-Mrówka spaces, define the concept of strongly $(\aleph_0, <\mathfrak c)$-separated almost disjoint families and prove the generic existence of completely separable strongly $(\aleph_0, <\mathfrak c)$-almost disjoint families assuming $\mathfrak s=\mathfrak c$ and $\mathfrak b=\mathfrak c$. We also provide an example of a Tychonoff almost-normal not normal pseudocompact space which is not countably compact, answering a question from P. Szeptycki and S. Garcia-Balan.

math.GN↗