arXiv subjects

Manuel Gonzalez

Publications and source records attributed to Manuel Gonzalez.

10 recordsLinked to original sources

arXiv2026

Embedding $\ell_2$ and $J$ into subspaces of $JT$ and $JT^*$

In the first part of the paper we show that every closed subspace of $JT$ or $JT^*$ contains $\ell_2$ complemented in $JT$ or $JT^*$ respectively, and $JT$ contains uncomplemented copies of $\ell_2$. As a result, the predual $\B$ of $JT$, as well as the spaces $JT$ and $JT^*$, are subprojective and superprojective. In the second part, we prove that every weakly Cauchy sequence that is not weakly convergent in $JT$ has a subsequence equivalent to the basis of $J$. Hence, every non-reflexive subspace of $JT$ contains an isomorphic copy of $J$, and every Schauder basic sequence in $JT$ has a subsequence which is equivalent either to the basis of $\ell_2$ or to the basis of $J$. Moreover these subspaces may be selected to be complemented in $JT$.

math.FA↗

arXiv2023

The Extreme Stellar-Signals Project III. Combining Solar Data from HARPS, HARPS-N, EXPRES, and NEID

We present an analysis of Sun-as-a-star observations from four different high-resolution, stabilized spectrographs -- HARPS, HARPS-N, EXPRES, and NEID. With simultaneous observations of the Sun from four different instruments, we are able to gain insight into the radial velocity precision and accuracy delivered by each of these instruments and isolate instrumental systematics that differ from true astrophysical signals. With solar observations, we can completely characterize the expected Doppler shift contributed by orbiting Solar System bodies and remove them. This results in a data set with measured velocity variations that purely trace flows on the solar surface. Direct comparisons of the radial velocities measured by each instrument show remarkable agreement with residual intra-day scatter of only 15-30 cm/s. This shows that current ultra-stabilized instruments have broken through to a new level of measurement precision that reveals stellar variability with high fidelity and detail. We end by discussing how radial velocities from different instruments can be combined to provide powerful leverage for testing techniques to mitigate stellar signals.

astro-ph.EP↗

arXiv2017

On separably injective Banach spaces and Corrigendum to "On separably injective Banach spaces" [Adv. Math. 234 (2013) 192--216]

In this paper we deal with two weaker forms of injectivity which turn out to have a rich structure behind: separable injectivity and universal separable injectivity. We show several structural and stability properties of these classes of Banach spaces. We provide natural examples of (universally) separably injective spaces, including $\mathcal L_\infty$ ultraproducts built over countably incomplete ultrafilters, in spite of the fact that these ultraproducts are never injective. We obtain two fundamental characterizations of universally separably injective spaces: a) A Banach space $E$ is universally separably injective if and only if every separable subspace is contained in a copy of $\ell_\infty$ inside $E$. b) A Banach space $E$ is universally separably injective if and only if for every separable space $S$ one has $\Ext(\ell_\infty/S, E)=0$. The final Section of the paper focuses on special properties of 1-separably injective spaces. Lindenstrauss\ obtained in the middle sixties a result that can be understood as a proof that, under the continuum hypothesis, 1-separably injective spaces are 1-universally separably injective; he left open the question in {\sf ZFC}. We construct a consistent example of a Banach space of type $C(K)$ which is 1-separably injective but not 1-universally separably injective. We show that, under the continuum hypothesis, "to be universally separably injective" is not a $3$-space property, as we wrongly claimed in the paper mentioned in the title.

math.FA↗

arXiv2016

GIARPS: the unique VIS-NIR high precision radial velocity facility in this world

GIARPS (GIAno & haRPS) is a project devoted to have on the same focal station of the Telescopio Nazionale Galileo (TNG) both the high resolution spectrographs HARPS-N (VIS) and GIANO (NIR) working simultaneously. This could be considered the first and unique worldwide instrument providing cross-dispersed echelle spectroscopy at a high resolution (R=115,000 in the visual and R=50,000 in the IR) and over in a wide spectral range (0.383 - 2.45 micron) in a single exposure. The science case is very broad, given the versatility of such an instrument and the large wavelength range. A number of outstanding science cases encompassing mainly extra-solar planet science starting from rocky planet search and hot Jupiters, atmosphere characterization can be considered. Furthermore both instrument can measure high precision radial velocity by means the simultaneous thorium technique (HARPS - N) and absorbing cell technique (GIANO) in a single exposure. Other science cases are also possible. Young stars and proto-planetary disks, cool stars and stellar populations, moving minor bodies in the solar system, bursting young stellar objects, cataclysmic variables and X-ray binary transients in our Galaxy, supernovae up to gamma-ray bursts in the very distant and young Universe, can take advantage of the unicity of this facility both in terms of contemporaneous wide wavelength range and high resolution spectroscopy.

astro-ph.IM↗

arXiv2011

Banach spaces of universal disposition

In this paper we present a method to obtain Banach spaces of universal and almost-universal disposition with respect to a given class $\mathfrak M$ of normed spaces. The method produces, among other, the Gurari\uı space $\mathcal G$ (the only separable Banach space of almost-universal disposition with respect to the class $\mathfrak F$ of finite dimensional spaces), or the Kubis space $\mathcal K$ (under {\sf CH}, the only Banach space with the density character the continuum which is of universal disposition with respect to the class $\mathfrak S$ of separable spaces). We moreover show that $\mathcal K$ is not isomorphic to a subspace of any $C(K)$-space -- which provides a partial answer to the injective space problem-- and that --under {\sf CH}-- it is isomorphic to an ultrapower of the Gurari\uı space. We study further properties of spaces of universal disposition: separable injectivity, partially automorphic character and uniqueness properties.

math.FA↗

arXiv1996

Factorization of weakly continuous holomorphic mappings

We prove a basic property of continuous multilinear mappings between topological vector spaces, from which we derive an easy proof of the fact that a multilinear mapping (and a polynomial) between topological vector spaces is weakly continuous on weakly bounded sets if and only if it is weakly {\it uniformly\/} continuous on weakly bounded sets. This result was obtained in 1983 by Aron, Hervés and Valdivia for polynomials between Banach spaces, and it also holds if the weak topology is replaced by a coarser one. However, we show that it need not be true for a stronger topology, thus answering a question raised by Aron. As an application of the first result, we prove that a holomorphic mapping $f$ between complex Banach spaces is weakly uniformly continuous on bounded subsets if and only if it admits a factorization of the form $f=g\circ S$, where $S$ is a compact operator and $g$ a holomorphic mapping.

math.FA↗

arXiv1994

Polynomial Grothendieck properties

A Banach space $E$ has the Grothendieck property if every (linear bounded) operator from $E$ into $c_0$ is weakly compact. It is proved that, for an integer $k>1$, every $k$-homogeneous polynomial from $E$ into $c_0$ is weakly compact if and only if the space ${\cal P}(^kE)$ of scalar valued polynomials on $E$ is reflexive. This is equivalent to the symmetric $k$-fold projective tensor product of $E$ (i.e., the predual of ${\cal P}(^kE)$) having the Grothendieck property. The Grothendieck property of the projective tensor product $E\widehat{\bigotimes}F$ is also characterized. Moreover, the Grothendieck property of $E$ is described in terms of sequences of polynomials. Finally, it is shown that if every operator from $E$ into $c_0$ is completely continuous, then so is every polynomial between these spaces.

math.FA↗

arXiv1994

When every polynomial is unconditionally converging

Letting $E$, $F$ be Banach spaces, the main two results of this paper are the following: (1) If every (linear bounded) operator $E\rightarrow F$ is unconditionally converging, then every polynomial from $E$ to $F$ is unconditionally converging (definition as in the linear case). (2) If $E$ has the Dunford-Pettis property and every operator $E\rightarrow F$ is weakly compact, then every $k$-linear mapping from $E^k$ into $F$ takes weak Cauchy sequences into norm convergent sequences. In particular, every polynomial from $\ell_\infty$ into a space containing no copy of $\ell_\infty$ is completely continuous. This solves a problem raised by the authors in a previous paper, where they showed that there exist nonweakly compact polynomials from $\ell_\infty$ into any nonreflexive space.

math.FA↗

arXiv1994

Unconditionally converging polynomials on Banach spaces

We prove that weakly unconditionally Cauchy (w.u.C.) series and unconditionally converging (u.c.) series are preserved under the action of polynomials or holomorphic functions on Banach spaces, with natural restrictions in the latter case. Thus it is natural to introduce the unconditionally converging polynomials, defined as polynomials taking w.u.C. series into u.c.\ series, and analogously, the unconditionally converging holomorphic functions. We show that most of the classes of polynomials which have been considered in the literature consist of unconditionally converging polynomials. Then we study several ``polynomial properties'' of Banach spaces, defined in terms of relations of inclusion between classes of polynomials, and also some ``holomorphic properties''. We find remarkable differences with the corresponding ``linear properties''. For example, we show that a Banach space $E$ has the polynomial property (V) if and only if the spaces of homogeneous scalar polynomials ${\cal P}(^k\!E)$, $k\in{\bf N}$, or the space of scalar holomorphic mappings of bounded type ${\cal H}_b(E),$ are reflexive. In this case the dual space $E^*$, like the dual of Tsirelson's space, is reflexive and contains no copies of $\ell_p$.

math.FA↗

arXiv1994

Representing non-weakly compact operators

For each $S \in L(E)$ (with $E$ a Banach space) the operator $R(S) \in L(E^{**}/E)$ is defined by $R(S)(x^{**}+E) = S^{**}x^{**}+E$ \quad ($x^{**}\in E^{**}$). We study mapping properties of the correspondence $S\to R(S),$ which provides a representation $R$ of the weak Calkin algebra $L(E)/W(E)$ (here $W(E)$ denotes the weakly compact operators on $E$). Our results display strongly varying behaviour of $R.$ For instance, there are no non--zero compact operators in Im$(R)$ in the case of $L^1$ and $C(0,1),$ but $R(L(E)/W(E))$ identifies isometrically with the class of lattice regular operators on $\ell^2$ for $E=\ell^2(J)$ (here $J$ is the James' space). Accordingly, there is an operator $T \in L(\ell^2(J))$ such that $R(T)$ is invertible but $T$ fails to be invertible modulo $W(\ell^2(J)).$

math.FA↗