Related papers: Lineability of the set of bounded linear non-absol…
In this note we answer a question concerning lineability of the set of non-absolutely summing operators.
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…
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…
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…
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…
In this paper we investigate the connections between the several different extensions of the concept of absolutely summing operators.
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.
In the present paper we give results on the closedness and the self-adjointness of the sum of two unbounded operators. We present a new approach to these fundamental questions in operator theory. We also prove a new version of the Fuglede…
Let $\mathscr{A}$ be a nonempty set of infinite matrices of linear operators between two topological vector spaces. We show that a sequence is uniformly $\mathscr{A}$-summable if and only if it is $B$-summable for all matrices $B$ of linear…
It is well known that not every summability property for non linear operators leads to a factorization theorem. In this paper we undertake a detailed study of factorization schemes for summing linear and nonlinear operators. Our aim is to…
We prove an uniform boundedness principle for the Lipschitz seminorm of continuous, monotone, positively homogeneous and subadditive mappings on suitable cones of functions. The result is applicable to several classes of classically…
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…
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…
Let $H$ be a real Hilbert space. In this short note, using some of the properties of bounded linear operators with closed range defined on $H$, certain bounds for a specific convex subset of the solution set of infinite linear…
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 the operators involved do not need to be linear.
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…
In the short note we prove that for every $0<p<1$, there exists an infinite dimensional closed linear subspace of $\mathcal{L}\left( \ell_{p};\ell_{p}\right) $ every nonzero element of which is non $(r,s)$-absolutely summing operator for…
It is well-known that the controllability of finite-dimensional nonlinear systems can be established by showing the controllability of the linearized system. However, this classical result does not generalize to infinite-dimensional…
We prove that the algebraic sum of unbounded normal operators satisfies the square root problem of Kato under appropriate hypotheses. As application, we consider perturbed Schrodinger operators.