Related papers: Volterra type integral and composition operators o…
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…
This paper is a sequel to [6]. In that paper we transferred the discussions in [1] and [13] concerning almost invariant half-spaces for operators on complex Banach spaces to the context of operators on Hilbert space, and we gave easier…
We survey recent results about composition operators induced by analytic self-maps of the unit disk in the complex plane on various Banach spaces of analytic functions taking values in infinite-dimensional Banach spaces. We mostly…
In this paper we consider composition operators on locally convex spaces of functions defined on $\mathbb{R}$. We prove results concerning supercyclicity, power boundedness, mean ergodicity and convergence of the iterates in the strong…
In this work, a connection between some spectral properties of direct integral of operators in the direct integral of Hilbert spaces and their coordinate operators has been investigated.
We extend existence and uniqueness results of [4] for nonlinear integro-differential equations of Volterra type between real locally complete vector spaces
Bounded composition operators in Paley-Wiener spaces have simple forms, and they are just operators composed through affine mappings of the complex plane. The purpose of this article is to explore some notions about bounded operators and…
We investigate the relationship between mapping cones and matrix ordered *-vector spaces (i.e., abstract operator systems). We show that to every mapping cone there is an associated operator system on the space of n-by-n complex matrices,…
Integral operators play an important role modeling various physical and biological processes. In this article we consider such a nonlinear integro-differential equation. We study several properties of equilibrium solutions of the operator…
We show that a class of models for particles with internal degrees of freedom are integrable. These systems are basically generalizations of the models of Calogero and Sutherland. The proofs of integrability are based on a recently…
In this article, we investigate the method of upper and lower solutions for Volterra integral equation of the first kind on arbitrary time scale $\mathbb{T}$. We establish some existence results in a certain sector. Moreover, monotone…
In this paper we introduce a very general setting dealing with the superposition of operators of any positive order and provide a systematic study of them. We also provide examples and counterexamples, as well as characterizing properties…
We present a treasure trove of open problems in matrix and operator inequalities, of a functional analytic nature, and with various degrees of hardness.
We investigate spaces of operators which are invariant under translations or modulations by lattices in phase space. The natural connection to the Heisenberg module is considered, giving results on the characterisation of such operators as…
The notions of expansivity and positive expansivity for composition operators on Orlicz spaces are investigated. In particular, necessary and sufficient conditions are given for a composition operator to be expansive, positively expansive,…
The present text surveys some relevant situations and results where basic Module Theory interacts with computational aspects of operator algebras. We tried to keep a balance between constructive and algebraic aspects.
This paper explores the Invariant Subspace Problem in operator theory and functional analysis, examining its applications in various branches of mathematics and physics. The problem addresses the existence of invariant subspaces for bounded…
\v{C}u\v{c}kovi\'{c} and Paudyal recently characterized the lattice of invariant subspaces of the shift plus a complex Volterra operator on the Hilbert space $H^2$ on the unit disk. Motivated by the idea of Ong, in this paper, we give a…
A new functional model for pairs of commuting isometries is described. Intertwining operators between such models are then studied in order to approach the classification of invariant subspaces of such pairs.
Let $\phi$ be an analytic self-map of the open unit disk $\mathbb{D}$ and $g$ analytic in $\mathbb{D}$. We characterize boundedness and compactness of generalized Volterra type integral operators $$GI_{(\phi,g)}f(z)=…