Related papers: Super-Shadowing and Supercyclicity

In this paper we study the dynamics of the composition operators defined in the Schwartz space $\mathcal{S}(\mathbb{R})$ of rapidly decreasing functions. We prove that such an operator is never supercyclic and, for monotonic symbols, it is…

We are concerned with surjectivity of perturbations of maximal monotone operators in non-reflexive Banach spaces. While in a reflexive setting, a classical surjectivity result due to Rockafellar gives a necessary and sufficient condition to…

This paper extends topics in linear algebra and operator theory for linear transformations on complex vector spaces to those on bicomplex Hilbert and Banach spaces. For example, Definition 3 for the first time defines a bicomplex vector…

Let $T$ be a so-called operator of Read's type on a (real or complex) separable Banach space, having no non-trivial invariant subset. We prove in this note that $T\oplus T$ is then hypercyclic, i.e. that $T$ satisfies the Hypercyclicity…

We consider abstract Banach spaces of analytic functions on general bounded domains that satisfy only a minimum number of axioms. We describe all invertible (equivalently, surjective) weighted composition operators acting on such spaces.…

We show that the multiples of the backward shift operator on the spaces $\ell_{p}$, $1\leq p<\infty$, or $c_{0}$, when endowed with coordinatewise multiplication, do not possess frequently hypercyclic algebras. More generally, we…

Let $\mathcal H$ be a complex infinite-dimensional separable Hilbert space, and let $\mathcal K(\mathcal H)$ be the $C^*$-algebra of compact linear operators in $\mathcal H$. Let $(E,\|\cdot\|_E)$ be a symmetric sequence space. If…

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…

It is proved that, if $(P_n)$ is a sequence of polynomials with complex coefficients having unbounded valences and tending to infinity at sufficiently many points, then there is an infinite dimensional closed subspace of entire functions,…

We show that if $T$ is a narrow operator on $X=X_{1}\oplus_{1} X_{2}$ or $X=X_{1}\oplus_{\infty} X_{2}$, then the restrictions to $X_{1}$ and $X_{2}$ are narrow and conversely. We also characterise by a version of the Daugavet property for…

We establish a spectral characterization theorem for the operators on complex Hilbert spaces of arbitrary dimensions that attain their norm on every closed subspace. The class of these operators is not closed under addition. Nevertheless,…

We consider the action of finitely truncated singular integral operators on functions taking values in a Banach space. Such operators are bounded for any Banach space, but we show a quantitative improvement over the trivial bound in any…

A bounded linear operator $T$ acting on a Banach space $\B$ is called weakly hypercyclic if there exists $x\in \B$ such that the orbit ${T^n x: n=0,1,...}$ is weakly dense in $\B$ and $T$ is called weakly supercyclic if there is $x\in \B$…

Depending on the behaviour of the complex-valued electromagnetic potential in the neighbourhood of infinity, pseudomodes of one-dimensional Dirac operators corresponding to large pseudoeigenvalues are constructed. This is a first systematic…

We consider random linear continuous operators $\Omega \to \mathcal{L}(\mathcal{X}, \mathcal{X})$ on a Banach space $\mathcal{X}$. For example, such random operators may be random quantum channels. The Law of Large Numbers is known when…

Based on the recently introduced uniform $\lambda-$adjustment for closed subspaces of Banach spaces we extend the concept of the strictly singular and finitely strictly singular operators to the sequences of closed subspaces and operators…

We first generalize the results of Le\'on and M\"uller [Studia Math. 175(1) 2006] on hypercyclic subspaces to sequences of operators on Fr\'echet spaces with a continuous norm. Then we study the particular case of iterates of an operator T…

In this paper, we are interested in the properties of a new class of operators, recently introduced by Shkarin, called strongly $n$-supercyclic operators. This notion is stronger than $n$-supercyclicity. We prove that such operators have…

A Banach space $X$ has the $2$-summing property if the norm of every linear operator from $X$ to a Hilbert space is equal to the $2$-summing norm of the operator. Up to a point, the theory of spaces which have this property is independent…

We study recurrent operators from a new perspective by introducing the notion of hyper-recurrent operators and establish robust connections with quasi-rigid operators. For example, we prove that a recurrent operator on a separable Banach…