Related papers: On summability of multilinear operators and applic…
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 of absolutely summing operators). However, these…
This paper investigates summability principles for multilinear summing operators. The main result presents a novel inclusion theorem for a class of summing operators, which generalizes several classical results. As applications, we derive…
This paper has a twofold purpose: to present an overview of the theory of absolutely summing operators and its different generalizations for the multilinear setting, and to sketch the beginning of a research project related to an objective…
The primary purpose of this paper is to investigate the question of invertibility of the sum of operators. The setting is bounded and unbounded linear operators. Some interesting examples and consequences are given. As an illustrative…
Advancements in mathematical programming have made it possible to efficiently tackle large-scale real-world problems that were deemed intractable just a few decades ago. However, provably optimal solutions may not be accepted due to the…
The purpose of this note is to survey a methodology to solve systems of polynomial equations and inequalities. The techniques we discuss use the algebra of multivariate polynomials with coefficients over a field to create large-scale linear…
Continuing previous work, this paper focuses on the summability problem of multivariate rational functions in the mixed case in which both shift and $q$-shift operators can appear. Our summability criteria rely on three ingredients…
This book is not meant to be another compendium of select inequalities, nor does it claim to contain the latest or the slickest ways of proving them. This project is rather an attempt at describing how most functional inequalities are not…
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 be useful in different practical problems. The second…
We prove a new result on multiple summing operators and among other applications, we provide a new extension of Littlewood's $4/3$ inequality to $m$-linear forms.
Across machine learning (ML) sub-disciplines, researchers make explicit mathematical assumptions in order to facilitate proof-writing. We note that, specifically in the area of fairness-accuracy trade-off optimization scholarship, similar…
We further develop the theoretical framework of proof mining, a program in mathematical logic that seeks to quantify and extract computational information from prima facie `non-computational' proofs from the mainstream mathematical…
We present an abstract result that characterizes the coincidence of certain classes of linear operators with the class of Cohen strongly summing linear operators. Our argument is extended to multilinear operators and, as a consequence, we…
Algorithms for continuous optimization problems have a rich history of design and innovation over the past several decades, in which mathematical analysis of their convergence and complexity properties plays a central role. Besides their…
The rationalizability concept was introduced in \cite{Ber84} and \cite{Pea84} to assess what can be inferred by rational players in a non-cooperative game in the presence of common knowledge. However, this notion can be defined in a number…
Unifying several directions of the development of the study of summing multilinear operators between Banach spaces, we construct a general framework that studies, under one single definition, multilinear operators that are summing with…
With the increasing pervasive use of machine learning in social and economic settings, there has been an interest in the notion of machine bias in the AI community. Models trained on historic data reflect biases that exist in society and…
Motivated by previous work leveraging factorizations of second- and fourth-order differential operators, a general integral inequality involving higher order derivatives is proven by elementary means. It is then shown how this framework…
Several matrix/operator inequalies are given. Most of them are unexpected extensions of the Araki Log-majorization theorem, obtained thanks to a new log-majorization for positive linear maps and normal operators (Theorem 2.9). The main idea…
Causality is a fundamental part of the scientific endeavour to understand the world. Unfortunately, causality is still taboo in much of psychology and social science. Motivated by a growing number of recommendations for the importance of…