Related papers: A note on lineability
In this note we solve, except for extremely pathological cases, a question posed by Puglisi and Seoane-Sepulveda on the lineability of the set of bounded non-absolutely summing linear operators. We also show how the idea of the proof can be…
In this note we prove an abstract version of a result from 2002 due to Delgado and Pi\~{n}ero on absolutely summing operators. Several applications are presented; some of them in the multilinear framework and some in a completely nonlinear…
In this note we introduce a new technique to answer an issue posed in [7] concerning geometric properties of the set of non-surjective linear operators. We also extend and improve a related result from the same paper.
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…
Among other results we investigate $\left( \alpha,\beta\right) $-lineability of the set of non-continuous $m$-linear operators defined between normed spaces as a subset of the space of all $m$-linear operators. We also give a partial answer…
In this short note we present some new results concerning cotype and absolutely summing multilinear operators.
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…
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…
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…
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.
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…
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.
Let $A,B\in B(H)$. In the present paper, we establish simple and interesting facts on when we have $|A||B|=|B||A|$, $|AB|=|A||B|$, $|A\pm B|\leq |A|+|B|$, $||A|-|B||\leq |A\pm B|$ and $\||A|-|B|\|\leq \|A\pm B\|$, where $|\cdot|$ denotes…
In this note, we shall give an improved lower bound for the argument of a power of a given algebraic number which has absolute value one but is not a root of unity.
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 improve a result of Bennett concerning certain sequences involving sums of powers of positive integers.
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…
We present maximality results in the setting of non necessarily bounded operators. In particular, we discuss and establish results showing when the "inclusion" between operators becomes a full equality.
Motivated by questions arising in the study of the spectral theory of models of aperiodic order, we investigate sums of functions of semibounded closed subsets of the real line. We show that under suitable thickness assumptions on the sets…