Related papers: An abstract result on Cohen strongly summing opera…
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…
Interrelation of the Coleman's representabilty theory for 1-density operators and abstract algebraic form of the Hohenberg-Kohn theorem is studied in detail. Convenient realization of the Hohenberg-Kohn set of classes of 1-electron…
Strongly irreducible operators can be considered as building blocks for bounded linear operators on complex separable Hilbert spaces. Many bounded linear operators can be written as direct sums of at most countably many strongly irreducible…
This is a continuation of the paper (quant-ph/0009012). In this letter we extend coherent operators and study some basic properties (the disentangling formula, resolution of unity, commutation relation, etc). We also propose a perspective…
A new construction for the form sum of positive, selfadjoint operators is given in this paper. The situation is a bit more general, because our aim is to add positive, symmetric operators. With the help of the used method, some commutation…
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.
We focus on the linear convergence of generalized proximal point algorithms for solving monotone inclusion problems. Under the assumption that the associated monotone operator is metrically subregular or that the inverse of the monotone…
In this note, we introduce generalized powers of linear operators. More precisely, operators are not raised to numbers but to other operators. We discuss several properties as regards this notion.
We consider the space of molecules endowed with the transpose version of the Chevet-Saphar norm and we identify its dual space with the space of Lipschitz strongly p-summing operators. We also extend some old results to the category of…
Consider a nonzero contraction $T$ and a bounded operator $X$ satisfying $TX=qXT$ for a complex number $q$. There are some interesting results in the literature on $q$-commuting dilation and $q$-commutant lifting of such pair $(T,X)$ when…
In this paper, we introduce a new class of positive linear operators that generalize the classical Bernstein operators. Specifically, we construct a sequence of operators that reproduce the logarithmic function $\ln(1+\mu+x)$, with $\mu >…
We consider sums of squares operators globally defined on the torus. We show that if some assumptions are satisfied the operators are globally analytic hypoelliptic. The purpose of the assumptions is to rule out the existence of a Hamilton…
Accretive and monotone operator theory are central branches of nonlinear functional analysis and constitute the abstract study of set-valued mappings between function spaces. This paper deals with the computational properties of certain…
Kwapie\'{n}'s theorem asserts that every continuous linear operator from $\ell_{1}$ to $\ell_{p}$ is absolutely $\left( r,1\right) $-summing for $1/r=1-\left\vert 1/p-1/2\right\vert .$ When $p=2$ it recovers the famous Grothendieck's…
We characterize those linear operators that can be expressed as a sum over k of terms of the form f_k(D) x^k and give several examples.
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.
We perform certain alternating binomial summations with parameters that occur in the analysis of algorithms. A combination of integral and special function and special number representations is used. The results are sufficiently general to…
At present an algebra of strongly interacting fields is unknown. In this paper it is assumed that the operators of strongly nonlinear field can form a non-associative algebra. It is shown that such algebra can be described as an algebra of…
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…
By extending the classical quantitative approximation results for positive and linear operators in $L^{p}([0, 1]), 1\le p \le +\infty$ of Berens and DeVore in 1978 and of Swetits and Wood in 1983 to the more general case of sublinear,…