Related papers: Narrow operators on lattice-normed spaces and vect…
Let $\Omega$ be a compact Hausdorff space, let $E$ be a Banach space, and let $C(\Omega, E)$ stand for the Banach space of all $E$-valued continuous functions on $\Omega$ under supnorm. In this paper we study when nuclear operators on…
We consider $C$-compact orthogonally additive operators in vector lattices. After providing some examples of $C$-compact orthogonally additive operators on a vector lattice with values in a Banach space we show that the set of those…
We prove that an order continuous Banach lattice E is a KB-space if and only if each positive compact operator on E is a KB operator. We give conditions on quasi-KB (resp., quasi-Levi) operators to be KB (resp., Levi), study norm…
We study continuity and boundedness of order-to-topology bounded and order-to topology continuous operators from ordered to topological vector spaces. Several results on automatic continuity of operators from ordered Frechet spaces to…
We give an overview of normality and conormality properties of pre-ordered Banach spaces. For pre-ordered Banach spaces $X$ and $Y$ with closed cones we investigate normality of $B(X,Y)$ in terms of normality and conormality of the…
This paper first gives a necessary and sufficient condition that a lattice $L$ can be represented as the collection of all up-sets of a poset. Applying the condition, it obtains a necessary and sufficient condition that a lattice can be…
While monotone operator theory is often studied on Hilbert spaces, many interesting problems in machine learning and optimization arise naturally in finite-dimensional vector spaces endowed with non-Euclidean norms, such as…
Let $\mathcal{H}$ be a Hilbert space, $L(\mathcal{H})$ the algebra of bounded linear operators on $\mathcal{H}$ and $W \in L(\mathcal{H})$ a positive operator. Given a closed subspace $\mathcal{S}$ of $\mathcal{H}$, we characterize the…
We establish that the Lie algebra of weight one states in a (strongly) rational vertex operator algebra is reductive, and that its Lie rank is bounded above by the effective central charge. We show that lattice vertex operator algebras may…
We prove a sharpened version of a conjecture of Dong-Mason about lattice subalgebras of a strongly regular vertex operator algebra $V$, and give some applications. These include the existence of a canonical conformal subVOA $W\otimes…
We study the fixed point problem for a system of multivariate operators that are coordinate-wise monotone (i.e., nondecreasing or nonincreasing in each of the variables, independently), in the setting of quasi-ordered sets. We show that…
This is an expository-survey on weak stability of bounded linear operators acting on normed spaces in general and, in particular, on Hilbert spaces. The paper gives a comprehensive account of the problem of weak operator stability,…
We apply to operator algebra theory a monotone selection principle which apparently escaped attention (of operator algebra theorists) so far. This principle relates to the basic order theoretic characterisation of von Neumann algebras given…
Our purpose in this note is to investigate the order properties of positive operators from a locally convex space into its conjugate dual. We introduce a natural generalization of the Busch-Gudder strength function and we prove Kadison's…
We show that even if a lattice Dirac operator satisfies the conditions consisting of locality, free of species doublings, correct continuum behavior, $\gm5$-hermiticity and the Ginsparg-Wilson relation, it does not necessarily have exact…
Mathematical morphology is a theory concerned with non-linear operators for image processing and analysis. The underlying framework for mathematical morphology is a partially ordered set with well-defined supremum and infimum operations.…
In this paper an idea of soft linear spaces and soft norm on soft linear spaces are given and some of their properties are studied. Soft vectors in soft linear spaces are introduced and their properties are studied. Completeness of soft…
We describe how self-adjoint ordered operator spaces, also called non-unital operator systems in the literature, can be understood as $*$-vector spaces equipped with a matrix gauge structure. We explain how this perspective has several…
Let $H_1,H_2$ be complex Hilbert spaces and $T$ be a densely defined closed linear operator (not necessarily bounded). It is proved that for each $\epsilon>0$, there exists a bounded operator $S$ with $\|S\|\leq \epsilon$ such that $T+S$ is…
We demonstrate that being a hyperbolicity preserver does not imply monotonicity for infinite order differential operators on $\mathbb{R}[x]$, thereby settling a recent conjecture in the negative. We also give some sufficient conditions for…