Related papers: Operators whose dual has non-separable range

In this note, we show that if a Banach space X has a predual, then every bounded linear operator on X with a continuous functional calculus admits a bounded Borel functional calculus. A consequence of this is that on such a Banach space,…

Let $X, Y$ be infinite dimensional, Banach spaces. Let $\mathcal{L}(X, Y)$ be the space of bounded operators . Motivated by the fact that smoothness of norm in the higher duals of even order of a Banach space can lead to Frechet…

We study octahedral norms in the space of bounded linear operators between Banach spaces. In fact, we prove that $L(X,Y)$ has octahedral norm whenever $X^*$ and $Y$ have octahedral norm. As a consequence the space of operators $L(\ell_1…

We show that there is an operator space notion of Lipschitz embeddability between operator spaces which is strictly weaker than its linear counterpart but which is still strong enough to impose linear restrictions on operator space…

In this article, the existence of the spectrum (the eigenvalues) for the nonlinear continuous operators acting in the Banach spaces is investigated. For the study, this question is used a different approach that allows the studying of all…

Let l be a Banach sequence space with a monotone norm in which the canonical system (e_{n}) is an unconditional basis. We show that if there exists a continuous linear unbounded operator between l-K\"{o}the spaces, then there exists a…

It is introduced an open class of linear operators on Banach and Hilbert spaces such that their non-wandering set is an infinite dimensional topologically mixing subspace. In certain cases, the non-wandering set coincides with the whole…

The notion of decomposable operators acting between distinct $L^p$-direct integrals of Banach spaces is introduced. We show that these operators generalize the composition operator, in sense that a mapping is replaced by a binary relation.…

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 characterize the spectrum of positive linear operators $T:X \to Y$, where $X$ and $Y$ are complex Banach function spaces with unit $1$, having finite rank and a partition of unity property. Then all the points in the spectrum are…

In this paper, we continue the investigation of topological properties of unbounded norm (un-)topology in normed lattices. We characterize separability and second countability of un-topology in terms of properties of the underlying normed…

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…

Given a Banach space $E$, we ask which closed subspaces may be realised as the kernel of a bounded operator $E \rightarrow E$. We prove some positive results which imply in particular that when $E$ is separable every closed subspace is a…

We answer, by counterexample, several open questions concerning algebras of operators on a Hilbert space. The answers add further weight to the thesis that, for many purposes, such algebras ought to be studied in the framework of operator…

In this paper we study sufficient conditions for an operator to have an almost-invariant half-space. As a consequence, we show that if $X$ is an infinite-dimensional complex Banach space then every operator $T\in\mathcal{L}(X)$ admits an…

The aim of this manuscript is to study \emph{spear operators}: bounded linear operators $G$ between Banach spaces $X$ and $Y$ satisfying that for every other bounded linear operator $T:X\longrightarrow Y$ there exists a modulus-one scalar…

Let $E$ and $F$ be Banach lattices. We show first that the disjointness preserving linear functionals separate the points of any infinite dimensional Banach lattice $E$, which shows that in this case the unbounded disjointness operators…

We consider linear bounded operators acting in Banach spaces with a basis, such operators can be represented by an infinite matrix. We prove that for an invertible operator there exists a sequence of invertible finite-dimensional operators…

Among other results we investigate $\left( \alpha,\beta\right) $-lineability of the set of non-continuous $m$-linear operators defined between normed spaces as a subset of the space of all $m$-linear operators. We also give a partial answer…

Theorem: Let X and Y be two Banach spaces, Phi: X to Y a continuous, linear, surjective operator, and Psi: X to Y a completely continuous operator with bounded range. Then, one has dim{x in X : Phi(x)=Psi(x)} >= dim(Phi^{-1}(0)). Here dim…