Related papers: $u\tau$-continuous operators on locally solid vect…
Recently, the functionals different types of unbounded convergences (uo, un, uaw, uaw*) in Banach lattices were studied. In this paper, we study the continuous operators with respect to unbounded convergences. We first investigate the…
We study modularity of the lattice Lat $(T)$ of closed invariant subspaces for a $C_0$-operator $T$ and find a condition such that Lat $(T)$ is a modular. Furthermore, we provide a quasiaffinity preserving modularity.
The local boundedness of classes of operators is analyzed on different subsets directly related to their Fitzpatrick functions and characterizations of the topological vector spaces for which that local boundedness holds is given in terms…
Let $x_\alpha$ be a net in a locally solid vector lattice $(X,\tau)$; we say that $x_\alpha$ is unbounded $\tau$-convergent to a vector $x\in X$ if $\lvert x_\alpha-x \rvert\wedge w \xrightarrow{\tau} 0$ for all $w\in X_+$. In this paper,…
Following several papers in the prior literature, we study the relationship between order bounded operators, topologically bounded operators and topologically continuous operators. Our main contribution is two folded: (i) we provide a set…
We treat some questions related to supercyclicity of continuous linear operators when acting in locally convex spaces. We extend results of Ansari and Bourdon and consider doubly power bounded operators in this general setting. Some…
The \emph{Continuity Problem} is the question whether effective operators are continuous, where an effective operator $F$ is a function on a space of constructively given objects $x$, defined by mapping construction instructions for $x$ to…
In this paper we consider unbounded weighted conditional type operators on the space Lp, we give some conditions under which they are densely defined and we obtain a dense subset of the domain. Also, we get that a WCT operator is continuous…
We construct and characterize tight binding Hamiltonians which contain a completely flat topological band made of continuum lowest Landau level wavefunctions sampled on a lattice. We find an infinite family of such Hamiltonians, with simple…
In this article we discuss the solvability of some class of fully nonlinear equations, and equations with p-Laplacian in more general conditions by using a new approach given in [1] for studying the nonlinear continuous operator. Moreover…
In this paper, we consider the locally convex spaces of entire functions with growth given by proximate orders, and study the representation as a differential operator of a continuous homomorphism from such a space to another one. As a…
We study properties of the topological space of composition operators on the Banach algebra of bounded functions on an unbounded, locally finite metric space in the operator norm topology and essential norm topology. Moreover, we…
An operator $T $ from a vector lattice $E$ into a normed lattice $F$ is called unbounded $\sigma$-order-to-norm continuous whenever $x_{n}\xrightarrow{uo}0$ implies $\| Tx_{n}\|\rightarrow 0$, for each sequence $(x_{n})_n\subseteq E$. For a…
Suppose $X$ is a locally solid vector lattice. In this paper, we introduce the notion "$AM$-property" in $X$ as an extension for $AM$-spaces in the category of all Banach lattices. With the aid of this concept, we characterize spaces in…
Suppose $X$ is a vector lattice and there is a notion of convergence $x_{\alpha} \rightarrow x$ in $X$. Then we can speak of an "unbounded" version of this convergence by saying that $(x_{\alpha})$ unbounded converges to $x\in X$ if $\lvert…
Consider a finite collection $\{T_1, \ldots, T_J\}$ of differential operators with constant coefficients on $\mathbb{T}^n$ ($n\geq 2$) and the space of smooth functions generated by this collection, namely, the space of functions $f$ such…
Consider the lattice of bounded linear operators on the space of Borel measures on a Polish space. We prove that the operators which are continuous with respect to the weak topology induced by the bounded measurable functions form a…
We study relatively uniformly continuous operator semigroups on ordered vector spaces and extend several recent results obtained by M. Kramar Fijavz, M. Kandic, M. Kaplin, and J. Gluck in the vector lattice setting to ordered vector spaces…
We exhibit a general class of unbounded operators in Banach spaces which can be shown to have the single-valued extension property, and for which the local spectrum at suitable points can be determined. We show that a local spectral radius…
In this paper we classify all topological vector spaces with linear topology with the property that all algebraic automorphisms are continuous. Moreover, we prove some properties of these spaces.