Related papers: Lineability and uniformly dominated sets of summin…
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…
A quasi-product on the normed space is defined. In addition, the notions of the eigenvectors of a linear operator can be extended for the nonlinear operator. Based on the quasi-product and the generalized eigenvectors, the spectral theorems…
We apply the geometric approach provided by $\Sigma$-operators to develop a theory of $p$-summability for multilinear operators. In this way, we introduce the notion of Lipschitz $p$-summing multilinear operators and show that it is…
The considered problem is uniform convergence of sequences of hypergeometric series. We give necessary and sufficient conditions for uniformly dominated convergence of infinite sums of proper bivariate hypergeometric terms. These conditions…
We use an interpolative technique from \cite{abps} to introduce the notion of multiple $N$-separately summing operators. Our approach extends and unifies some recent results; for instance we recover the best known estimates of the…
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…
In this paper we derive novel families of inclusion sets for the spectrum and pseudospectrum of large classes of bounded linear operators, and establish convergence of particular sequences of these inclusion sets to the spectrum or…
The nonlinear geometry of operator spaces has recently started to be investigated. Many notions of nonlinear embeddability have been introduced so far, but, as noticed before by other authors, it was not clear whether they could be…
Lineability is a property enjoyed by some subsets within a vector space X. A subset A of X is called lineable whenever A contains, except for zero, an infinite dimensional vector subspace. If, additionally, X is endowed with richer…
Linear operators preserving the direct sum of polynomial rings P(m)\oplus P(n) are constructed. In the case |m-n|=1 they correspond to atypical representations of the superalgebra osp(2,2). For |m-n|=2 the generic, finite dimensional…
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…
We show that given a positive integer $m$, a real number $p\in\left[ 2,\infty\right)$ and $1\leq s<p^{\ast}$ the set of non--multiple $\left( r;s\right)$--summing $m$--linear forms on $\ell_{p}\times\cdots\times \ell_{p}$ contains, except…
We prove bounds for multilinear operators on $\R^d$ given by multipliers which are singular along a $k$ dimensional subspace. The new case of interest is when the rank $k/d$ is not an integer. Connections with the concept of {\em true…
In this paper we introduce the concept of infinite pointwise dense lineability (spaceability), and provide a criterion to obtain density from mere lineability. As an application, we study the linear and topological structures within the set…
Recently, Liu, Moursi and Vanderwerff have introduced the class of super strongly nonexpansive mappings as a counterpart to operators which are maximally monotone and uniformly monotone. We give a quantitative study of these notions in the…
We prove a general factorization theorem for Lipschitz summing operators in the context of metric spaces which recovers several linear and nonlinear factorization theorems that have been proved recently in different environments. New…
In this paper, we study infinite dimensional stochastic systems having both unbounded control and observation operators. First of all, using a semigroup approach, we give another take of the well-posedness of such systems treated in [SIAM…
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…
Complementable operators extend classical matrix decompositions, such as the Schur complement, to the setting of infinite-dimensional Hilbert spaces, thereby broadening their applicability in various mathematical and physical contexts. This…
Our main theorem is in the generality of the axioms of Hilbert space, and the theory of unbounded operators. Consider two Hilbert spaces such that their intersection contains a fixed vector space D. It is of interest to make a precise…