Searcharxiv⌕ Search

arXiv subjects

Jamilson R. Campos

Publications and source records attributed to Jamilson R. Campos.

9 recordsLinked to original sources
arXiv2026

Geometric spaceability in sequence classes and operator ideals

This paper investigates advanced notions of lineability and spaceability within the frameworks of sequence spaces and operator ideals. We propose the notion of \emph{Standard Sequence Classes} to provide an environment that unifies numerous classical sequence spaces while preserving their fundamental behavior. Utilizing this framework, we establish general $(α, \mathfrak{c})$-spaceability results for complements of unions of (quasi-)Banach sequence spaces. These results extend the existing literature by addressing the geometrically more demanding case where $α> 1$ and by encompassing the non-locally convex (quasi-)Banach setting. Furthermore, we provide criteria for the pointwise $\mathfrak{c}$-spaceability of differences between general operator ideals with values in standard sequence spaces. Our results recover and improve several known findings in the context of vector-valued sequences.

math.FA↗
arXiv2024

An injective-type norm and integral bilinear forms defined by sequence classes

In this work we define a class of injective-type norm on tensor products through the environment of sequence classes. Examples and results on this norm will be presented and the duality is studied in this context. As a byproduct, we present the definition of the associated integral-type bilinear forms and also a tensor characterization for a class of sequence spaces.

math.FA↗
arXiv2022

Maximal ideals of generalized summing linear operators

We prove when a Banach ideal of linear operators defined, or characterized, by the transformation of vector-valued sequences is maximal. Known results are recovered as particular cases and new information is obtained. To accomplish this task we study a tensor quasi-norm determined by the underlying sequence classes. The duality theory for these tensor quasi-norms is also developed.

math.FA↗
arXiv2022

An anisotropic summability and mixed sequences

In this paper we define and study a vector-valued sequence space, called the space of anisotropic $(s,q,r)$-summable sequences, that generalizes the classical space of $(s; q)$-mixed sequences (or mixed $(s; q)$-summable sequences). Furthermore, we define two classes of linear operators involving this new space and one of them generalizes the class of $(s; q) $-mixed linear operators due A. Pietsch. Some characterizations, inclusion results and a Pietsch domination-type theorem are presented for these classes. It is worth mentioning that some of these results are new even in the particular cases of mixed summable sequences and mixed summing operators.

math.FA↗
arXiv2020

Duality theory for generalized summing linear operators

Generalizing classical results of the theory of absolutely summing operators, in this paper we characterize the duals of a quite large class of Banach operator ideals defined or characterized by the transformation of vector-valued sequences.

math.FA↗
arXiv2018

Mid summable sequences: an anisotropic approach

The notion of mid $p$-summable sequences was introduced by Karn and Sinha in 2014 and recently explored and expanded by Botelho, Campos and Santos in 2017. In this paper we design a theory of mid summable sequences in the anisotropic setting defining a new more general space called space of mid $(q,p)$-summable sequences. As a particular case of our results, we prove an inclusion relation between spaces of mid summable sequences. We also define classes of operators that deals with this new space, the mid $(q,p)$-summing operators, and prove some important results on these classes as inclusion and coincidence theorems and a Pietsch Domination-type theorem. It is worth to mentioning that these abovementioned results are new even in the particular case of the mid $p$-summable environment.

math.FA↗
arXiv2015

Type and cotype of multilinear operators

The aim of this paper is to start the study of multilinear generalizations of the classical ideals of linear operators of type $p$ and cotype $q$. As a first step in a theory we believe will be long and fruitful, we propose a notion of type and cotype of multilinear operators and the resulting classes of such mappings are studied in the setting of the theory of Banach/quasi-Banach ideals of multilinear operators. Distinctions between the linear and the multilinear theories are pointed out, typical multilinear features of the theory are emphasized and many illustrative examples are provided. The classes we introduce are related to the multi-ideals generated by the linear ideals of operators of some type/cotype and are proved to be maximal and Aron-Berner stable.

math.FA↗
arXiv2015

Operator ideals related to absolutely summing and Cohen strongly summing operators

We study the ideals of linear operators between Banach spaces determined by the transformation of vector-valued sequences involving the new sequence space introduced by Karn and Sinha \cite{karnsinha} and the classical spaces of absolutely, weakly and Cohen strongly summable sequences. As applications, we prove a new factorization theorem for absolutely summing operators and a contribution to the existence of infinite dimensional spaces formed by non-absolutely summing operators is given.

math.FA↗