Related papers: Unbounded operators on Banach spaces over the quat…

We construct an example of a real Banach space whose group of surjective isometries has no uniformly continuous one-parameter semigroups, but the group of surjective isometries of its dual contains infinitely many of them. Other examples…

In this article we extend the notion of quasi-nilpotent equivalent operators, introduced by Colojoara and Foias \cite{co1} for Banach spaces, to the class of bounded operators on sequentially complete locally convex spaces.

In this note, we introduce and study the left (right) pseudospectrum and left (right) condition pseudospectrum of bounded linear operators on ultrametric Banach spaces. We prove some results about them.

Motivated by a seminal paper of professor M. Z. Nashed published in 1987 on classification of ill-posed linear operator equations and distinguishing two types of ill-posedness in Banach and Hilbert spaces, we present, illustrate and justify…

We show that any bounded operator $T$ on a separable, reflexive, infinite-dimensional Banach space $X$ admits a rank one perturbation which has an invariant subspace of infinite dimension and codimension. In the non-reflexive spaces, we…

We analyse the one-loop dilatation operator with the help of the Brauer algebra. We find some BPS operators in N=4 SYM, which are labelled by irreducible representations of the Brauer algebra. Some of them are quarter BPS operators. The…

We consider weakly closed transitive algebras of operators containing non-zero compact operators in real Banach spaces (Lomonosov algebras). It is shown that they are naturally divided in three classes: the algebras of real, complex and…

We consider a Hilbert space that is a product of a finite number of Hilbert spaces and operators that are represented by "componental operators" acting on the Hilbert spaces that form the product space. We attribute operatorial properties…

We prove the existence of the invariant subspaces of some operators in a real Banach space. For example, linear isometries have invariant subspaces

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…

In this paper we extend Korovkin's theorem to the context of sequences of weakly nonlinear and monotone operators defined on certain Banach function spaces. Several examples illustrating the theory are included.

Unbounded composition operators in $L^2$-space over discrete measure spaces are investigated. Normal, formally normal and quasinormal composition operators acting in $L^2$-spaces of this kind are characterized.

We establish a characterization of doubly power-bounded elements with finite spectrum in Banach algebras. In particular, we present a spectral decomposition for such elements, extending a classical theorem of Gelfand concerning doubly…

We work with very general Banach spaces of analytic functions in the disk or other domains which satisfy a minimum number of natural axioms. Among the preliminary results, we discuss some implications of the basic axioms and identify all…

One-parameter strongly continuous semigroups of linear bounded operators on Banach spaces (also known as $C_0$-semigroups) are a fundamental operator-theoretic tool used in the study of linear and non-linear evolution PDEs arising in…

Motivated by the equivalent definition of a continuous operator between Banach spaces in terms of weakly null nets, we introduce unbounded continuous operators by replacing weak convergence with the unbounded absolutely weak convergence (…

In the paper is considered two problems on extension of operators whose range space for the first problem (or domain space for the second one) belongs to the fixed class of finite equivalence, which is generated by a given Banach space $X$.…

We study the Banach algebras of bounded holomorphic functions on the unit disk whose boundary values, having, in a sense, the weakest possible discontinuities, belong to the algebra of semi-almost periodic functions on the unit circle. The…

A bounded linear operator $T$ on a Banach space $X$ is called subspace-hypercyclic if there is a subspace $M \subsetneq X$ and a vector $x \in X$ such that $orb{(x,T)} \cap M$ is dense in $M$. We show that every Banach space supports…

This article introduces classes of normal and unitary operators on smooth Banach spaces, providing extensions of the classical notions of normal and unitary operators from Hilbert spaces to the smooth Banach space setting. The proposed…