Related papers: Multiple almost summing operators
In this note we explore the notion of everywhere almost summing polynomials and define a natural norm which makes this class a Banach multi-ideal which is a holomorphy type (in the sense of L.Nachbin) and also coherent and compatible (in…
We construct a general framework that generates classes of multilinear operators between Banach spaces which encompasses, as particular cases, the several classes of summing type multilinear operators that have been studied individually in…
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…
In this short note we present some new results concerning cotype and absolutely summing multilinear operators.
In this paper we provide an abstract aproach to the study of classes of multiple summing multilinear operators between Banach spaces. The main purpose is unify the study of several known classes and results, for example multiple $(p,…
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…
In this paper we investigate the connections between the several different extensions of the concept of absolutely summing operators.
In this paper we introduce an abstract approach to the notion of absolutely summing multilinear operators. We show that several previous results on different contexts (absolutely summing, almost summing, Cohen summing) are particular cases…
Cotype is used in this paper to prove new results concerning the existence of non-absolutely summing linear operators between Banach spaces. We derive consequences that extend/generalize/ complement some classic results. We also point out…
We introduce and develop the notion of hyper-ideals of multilinear operators between Banach spaces. While the well studied notion of ideals of multilinear operators (multi-ideals) relies on the composition with linear operators, the notion…
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 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…
Considering the successful theory of multiple summing multilinear operators as a prototype, we introduce the classes of multiple Cohen strongly p-summing multilinear operators and polynomials. The adequacy of these classes under the…
In the nonlinear field of multilinear operators and homogeneous polynomials between Banach spaces, we develop a technique, based on the transformation of vector-valued sequences, to create new examples of hyper-ideals of multilinear…
We investigate lineability/spaceability problems within the setting of multilinear summing operators on quasi-Banach sequence spaces. Furthermore, we deal with the contemporary geometric notions of pointwise-lineability and…
We prove new summability properties for multilinear operators on $\ell_p$ spaces. An important tool for this task is a better understanding of the interplay between almost summing and absolutely summing multilinear operators.
Let $X_1, \ldots, X_n,Y$ be classes of Banach spaces-valued sequences. An $n$-linear operator $A$ between Banach spaces belongs to the ideal of $(X_1, \ldots, X_n;Y)$-summing multilinear operators if $(A(x_j^1, \ldots, x_j^n))_{j=1}^\infty$…
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…
We introduce and explore the concept of positive ideals for both linear and multilinear operators between Banach lattices. This paper delineates the fundamental principles of these new classes and provides techniques for constructing…
This short note has a twofold purpose: (i) to solve the question that motivates a recent paper of D. Popa on multilinear variants of Pietsch's composition theorem for absolutely summing operators. More precisely, we remark that there is a…