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Manuel González

Publications and source records attributed to Manuel González.

At least 19 recordsLinked to original sources
arXiv2026

Grothendieck and $\ell_\infty$-Grothendieck subspaces of $\ell_\infty$

Let $\mathfrak{c}=2^{\aleph_0}$. We prove that $\ell_\infty$ contains $2^{\mathfrak{c}}$ pairwise non-isomorphic non-reflexive Grothendieck subspaces. They may all be chosen to contain the canonical copy of $c_0$ and to have infinite-dimensional reflexive quotient. This is optimal and answers by the authors in 2021. We also show that the relative $\ell_\infty$-Grothendieck property depends on the specified copy of $c_0$ and is not an isomorphic invariant of the subspace. More generally, for every closed $E\subseteq\ell_\infty$ there is an $\ell_\infty$-Grothendieck subspace isomorphic to $\ell_\infty\oplus_\infty E$; taking $E=c_0$ answers a problem by González et al.

math.FA↗
arXiv2026

Tauberian pairs of closed subspaces of a Banach space

We introduce the notions of tauberian, cotauberian and weakly compact pair of closed subspaces of a Banach space. The theory produced by these notions is richer than that of the corresponding operators since an operator can be regarded as a suitable pair of closed subspaces. We investigate into these classes of pairs of subspaces and describe several applications in order to define some notions of indecomposability for Banach spaces and in order to extend definitions from the case of bounded operators to the case of closed operators.

math.FA↗
arXiv2026

A semi-coherent search for optical pulsations from Scorpius X-1

The emission of continuous gravitational waves (CWs) possibly explains why pulsars spinning with a period shorter than a millisecond have not been observed so far. Neutron stars accreting mass at the highest rates are the most promising targets for a search for CWs, because a strong emission of gravitational waves is required to balance the torque exerted by mass accretion onto the neutron star. Detecting coherent pulsations in the electromagnetic emission maximizes the search sensitivity, but has so far not been successful for most of the brightest accreting neutron stars. Here, we present the first search for pulsations in the optical band from the brightest accreting neutron star known, Sco X-1. To this end, we tailored semi-coherent search strategies to data obtained over four years, for a total of $\sim$$56$ ks, by the SiFAP2 fast photometer mounted at the Telescopio Nazionale Galileo (TNG). These searches are especially suited to analysing long observations of systems for which only limited knowledge on the orbital parameters is available, and involve joining coherent analyses on shorter segments without connecting the spin phase between them. The large count rates afforded by an optical telescope and the efficiency of the search strategy employed allowed us to set an upper limit of $9 \times 10^{-5}$ to the pulsed amplitude, which is lower by a factor of four with respect to previous searches in the X-ray band. We also show that the application of semi-coherent searches to SiFAP2 observations of the first detected optical millisecond pulsar, PSR J1023+0038, could have preceded its detection in the radio band. These results highlight the role played by high-time-resolution optical observations in performing deep searches of quickly rotating pulsars.

astro-ph.HE↗
arXiv2025

The Extreme Points of the Unit Ball of the James space $J$ and its dual spaces

We provide a new proof of S. Bellenot's characterization of the extreme points of the unit ball $B_J$ of James quasi-reflexive space $J$. We also provide an explicit description of the norm of $J^{**}$ which yields an analogous characterization for the extreme points of $B_{J^{**}}$. In the last part of the paper we describe the set of all extreme points of $B_{J^*}$ and its norm closure. It is remarkable that the descriptions of the extreme points of $B_J$ and $B_{J^*}$ are closely connected.

math.FA↗
arXiv2023

Complemented subspaces of $J$-sums of Banach spaces

We study the complemented subspaces of the $J$-sums of Banach spaces $J(Φ)$ and $\hat J(Φ)$ introduced by Bellenot. As an application, we show that, under some conditions, $J(Φ)$ and $\hat J(Φ)$ are subprojective, i.e., every closed infinite-dimensional subspace of either of them contains a complemented infinite-dimensional subspace.

math.FA↗
arXiv2023

The structure of Rochberg spaces

We study the structure of the Rochberg Banach spaces $\mathfrak Z_n$ associated to the interpolation pair $(\ell_\infty, \ell_1)$ at $1/2$, and the operators defined on them

math.FA↗
arXiv2023

Two classes of operators related to the perturbation classes problem

Let $SS$ and $SC$ be the strictly singular and the strictly cosingular operators acting between Banach spaces, and let $PΦ_+$ and $PΦ_+$ be the perturbation classes for the upper and the lower semi-Fredholm operators. We study two classes of operators $ΦS$ and $ΦC$ that satisfy $SS\subset ΦS \subset PΦ_+$ and $SC\subset ΦC\subset PΦ_-$. We give some conditions under which these inclusions become equalities, from which we derive some positive solutions to the perturbation classes problem for semi-Fredholm operators.

math.FA↗
arXiv2023

Disjointly non-singular operators: Extensions and local variations

The disjointly non-singular ($DNS$) operators $T\in L(E,Y)$ from a Banach lattice $E$ to a Banach space $Y$ are those operators which are strictly singular in no closed subspace generated by a disjoint sequence of non-zero vectors. When $E$ is order continuous with a weak unit, $E$ can be represented as a dense ideal in some $L_1(μ)$ space, and we show that each of $T\in DNS(E,Y)$ admits an extension $\overline{T}\in DNS(L_1(μ),PO)$ from which we derive that both $T$ and $T^{**}$ are tauberian operators and that the operator $T^{co}: E^{**}/E\to Y^{**}/Y$ induced by $T^{**}$ is an (into) isomorphism. Also, using a local variation of the notion of $DNS$ operator, we show that the ultrapowers of $T\in DNS(E,Y)$ are also $DNS$ operators. Moreover, when $E$ contains no copies of $c_0$ and admits a weak unit, we show that $T\in DNS(E,Y)$ implies $T^{**}\in DNS(E^{**},Y^{**})$.

math.FA↗
arXiv2023

Interpolator symmetries and new Kalton-Peck spaces

Diagrams generated by three interpolators in an abstract Kalton-Montgomery complex like interpolation scheme. We will consider in detail the case of the first three Schechter interpolators associated to the usual Calderón complex interpolation method in two especially interesting cases: weighted $\ell_2$ spaces, i.e., interpolation pairs $(\ell_2(w^{-1}), \ell_2(w))_θ$, and $\ell_p$ spaces, i.e., the interpolation pair $(\ell_\infty, \ell_1)_θ$, both at $θ=1/2$.

math.FA↗
arXiv2022

Operators on the Kalton-Peck space $Z_2$

We study operators on the Kalton-Peck Banach space $Z_2$ from various points of view: matrix representations, examples, spectral properties and operator ideals. For example, we prove that there are non-compact, strictly singular operators acting on $Z_2$, but the product of two of them is a compact operator. Among applications, we show that every copy of $Z_2$ in $Z_2$ is complemented, and each semi-Fredholm operator on $Z_2$ has complemented kernel and range, the space $Z_2$ is $Z_2$-automorphic and we give a partial solution to a problem of Johnson, Lindenstrauss and Schetchman about strictly singular perturbations of operators on $Z_2$.

math.FA↗
arXiv2022

Quasilinear duality and inversion in Banach spaces

We present a unified approach to the processes of inversion and duality for quasilinear and $1$-quasilinear maps; in particular, for centralizers and differentials generated by interpolation methods.

math.FA↗
arXiv2021

A quantitative approach to disjointly non-singular operators

We introduce and study some operational quantities which characterize the disjointly non-singular operators from a Banach lattice $E$ to a Banach space $Y$ when $E$ is order continuous, and some other quantities which characterize the disjointly strictly singular operators for arbitrary $E$.

math.FA↗
arXiv2021

Grothendieck spaces: the landscape and perspectives

In 1973, Diestel published his seminal paper `Grothendieck spaces and vector measures' that drew a connection between Grothendieck spaces (Banach spaces for which weak- and weak*-sequential convergences in the dual space coincide) and vector measures. This connection was developed in his book with J. Uhl Jr. `Vector measures'. Additionally, Diestel's paper included a section with several open problems about the structural properties of Grothendieck spaces, and only half of them have been solved to this day. The present paper aims at synthetically presenting the state of the art at subjectively selected corners of the theory of Banach spaces with the Grothendieck property, describing the main examples of spaces with this property, recording the solutions to Diestel's problems, providing generalisations/extensions or new proofs of various results concerning Grothendieck spaces, and adding to the list further problems that we believe are of relevance and may reinvigorate a better-structured development of the theory.

math.FA↗
arXiv2020

On $\ell_\infty$-Grothendieck subspaces

A closed subspace $S$ of $\ell_\infty$ is said to be a \emph{$\ell_\infty$-Grothendieck subspace} if $c_0\subset S$ (hence $\ell_\infty\subset S^{**}$) and every $σ(S^*,S)$-convergent sequence in $S^*$ is $σ(S^*,\ell_\infty)$-convergent. Here we give examples of closed subspaces of $\ell_\infty$ containing $c_0$ which are or fail to be $\ell_\infty$-Grothendieck.

math.FA↗
arXiv2020

Disjointly non-singular operators on Banach lattices

An operator $T$ from a Banach lattice $E$ into a Banach space is disjointly non-singular ($DN$-$S$, for short) if no restriction of $T$ to a subspace generated by a disjoint sequence is strictly singular. We obtain several results for $DN$-$S$ operators, including a perturbative characterization. For $E=L_p$ ($1< p<\infty$) we improve the results, and we show that the $DN$-$S$ operators have a different behavior in the cases $p=2$ and $p\neq 2$. As an application we prove that the strongly embedded subspaces of $L_p$ form an open subset in the set of all closed subspaces.

math.FA↗
arXiv2020

The perturbation classes problem for subprojective and superprojective Banach spaces

We show that the perturbation class for the upper semi-Fredholm operators between two Banach spaces X and Y coincides with the strictly singular operators when X is subprojective and that the perturbation class for the lower semi-Fredholm operators coincides with the strictly cosingular operators when Y is superprojective. Similar results were previously obtained under stronger conditions for X and Y.

math.FA↗