33 citations · 75 across the 21 of their papers we have counts for
24 papers
Similarities and differences between real and complex Banach spaces: an overview and recent developments
M. S. Moslehian, G. A. Muñoz-Fernández, A. M. Peralta +1
There are numerous cases of discrepancies between results obtained in the setting of real Banach spaces and those obtained in the complex context. This article is a modern expositi…
Dichotomy between operators acting on finite and infinite dimensional Hilbert spaces
L. Bernal-González, M. S. Moslehian, J. B. Seoane-Sepúlveda
In this expository article, we give several examples showing how drastically different can be the behavior of operators acting on finite versus infinite dimensional Hilbert spaces.…
Multiplicative structures of hypercyclic functions for convolution operators
Luis Bernal-González, J. Alberto Conejero, George Costakis +1
In this note, it is proved the existence of an infinitely generated multiplicative group consisting of entire functions that are, except for the constant function 1, hypercyclic wi…
On inequalities for convex functions
Luis Bernal-González, Pablo Jiménez-Rodríguez, Gustavo Adolfo Muñoz-Fernández +1
We study some properties convex functions fulfill. Among the conclusions we obtain from such result, we are able to prove some nontrivial inequalities among real numbers, and we gi…
Lineability in sequence and function spaces
G. Araújo, L. Bernal-González, G. A. Muñoz-Fernández +2
It is proved the existence of large algebraic structures \break --including large vector subspaces or infinitely generated free algebras-- inside, among others, the family of Lebes…
Estimates on the norm of polynomials and applications
Gustavo Araújo, Pablo Jiménez-Rodríguez, Gustavo A. Muñoz-Fernández +1
In this paper, equivalence constants between various polynomial norms are calculated. As an application, we also obtain sharp values of the Hardy--Littlewood constants for -homo…
Polynomial inequalities on the -circle sector
G. Araújo, P. Jiménez-Rodríguez, G. A. Muñoz-Fernández +1
A number of sharp inequalities are proved for the space of 2-homogeneous polynomials on endowed with the suprem…
Hölder's inequality: some recent and unexpected applications
N. Albuquerque, G. Araujo, D. Pellegrino +1
Hölder's inequality, since its appearance in 1888, has played a fundamental role in Mathematical Analysis and it is, without any doubt, one of the milestones in Mathematics. It may…
Optimal Hardy-Littlewood type inequalities for polynomials and multilinear operators
Nacib Albuquerque, Frédéric Bayart, Daniel Pellegrino +1
In this paper we obtain quite general and definitive forms for Hardy-Littlewood type inequalities. Moreover, when restricted to the original particular cases, our approach provides…
An interpolation technique towards the subpolynomial constants in the multilinear Bohnenblust-Hille inequality
Daniel Pellegrino, Juan B. Seoane-Sepúlveda
We show that a recent interpolative new proof of the Bohnenblust--Hille inequality, when suitably handled, recovers its best known constants. This seems to be unexpectedly surprisi…
Lineability, spaceability, and additivity cardinals for Darboux-like functions
Krzysztof Chris Ciesielski, José L. Gámez-Merino, Daniel Pellegrino +1
We introduce the concept of {\em maximal lineability cardinal number}, $\mL(M)$, of a subset of a topological vector space and study its relation to the cardinal numbers known…
Basic sequences and spaceability in spaces
Daniel Cariello, Juan B. Seoane-Sepúlveda
Let be a sequence space and denote by the subset of formed by sequences having only a finite number of zero coordinates. We study algebraic properties of and…
On nonlinear absolutely summing maps
D. Pellegrino, J. B. Seoane-Sepulveda
It is shown that the ultimate version of the nonlinear Pietsch Domination Theorem remains true, even in a stronger presentation, if one of its hypotheses is removed. More precisely…
On the optimality of the hypercontractivity of the complex Bohnenblust--Hille inequality
J. R. Campos, G. A. Muñoz-Fernández, D. Pellegrino +1
The main motivation of this paper is the following open problem: Is the hypercontractivity of the \emph{complex} polynomial Bohnenblust--Hille inequality an optimal result? We show…
A geometric technique to generate lower estimates for the constants in the Bohnenblust--Hille inequalities
G. A. Muñoz-Fernández, D. Pellegrino, J. Ramos Campos +1
The Bohnenblust--Hille (polynomial and multilinear) inequalities were proved in 1931 in order to solve Bohr's absolute convergence problem on Dirichlet series. Since then these ine…
On the hypercontractivity of the Bohnenblust-Hille inequality for homogeneous polynomials
Daniel Pellegrino, Juan B. Seoane-Sepúlveda
This paper has been withdrawn by the authors due to a crucial gap in the estimates for m>=4.
A general Extraplolation Theorem for absolutely summing operators
Daniel Pellegrino, Joedson Santos, Juan B. Seoane-Sepúlveda
In this note we prove a general version of the Extrapolation Theorem, extending the classical linear extrapolation theorem due to B. Maurey. Our result shows, in particular, that t…
Lower bounds for the constants in the Bohnenblust-Hille inequality: the case of real scalars
Diogo Diniz, Gustavo Muñoz-Fernández, Daniel Pellegrino +1
The Bohnenblust-Hille inequality was obtained in 1931 and (in the case of real scalars) asserts that for every positive integer and every -linear mapping $T:\ell_{\infty}^{N…
Algebrability, non-linear properties, and special functions
Artur Bartoszewicz, Szymon Glab, Daniel Pellegrino +1
We construct uncountably generated algebras inside the following sets of special functions: Sierpiński-Zygmund functions, perfectly everywhere surjective functions and nowhere cont…
Absolutely summing operators revisited: new directions in the nonlinear theory
Adriano Thiago Bernardino, Daniel Pellegrino, Juan B. Seoane-Sepúlveda +1
In the last decades many authors have become interested in the study of multilinear and polynomial generalizations of families of operator ideals (such as, for instance, the ideal…
Bounded and unbounded polynomials and multilinear forms: Characterizing continuity
José L. Gámez-Merino, Gustavo A. Muñoz-Fernández, Daniel Pellegrino +1
In this paper we prove a characterization of continuity for polynomials on a normed space. Namely, we prove that a polynomial is continuous if and only if it maps compact sets into…
Some improvements on the constants for the real Bohnenblust-Hille inequality
Daniel Pellegrino, Juan B. Seoane-Sepúlveda
A classical inequality due to Bohnenblust and Hille states that for every and every -linear mapping $U:\ell_{\infty}^{N}\times...\times\ell_{\infty}^{N}\right…
New upper bounds for the constants in the Bohnenblust-Hille inequality
Daniel Pellegrino, Juan B. Seoane-Sepúlveda
A classical inequality due to Bohnenblust and Hille states that for every positive integer there is a constant so that $$(\sum\limits_{i_{1},...,i_{m}=1}^{N}|U(e_{i_{…
Some techniques on nonlinear analysis and applications
Daniel Pellegrino, Joedson Santos, Juan B. Seoane-Sepúlveda
In this paper we present two different results in the context of nonlinear analysis. The first one is essentially a nonlinear technique that, in view of its strong generality, may…