Related papers: On Spaceability within Linear Dynamics
A classical result of Sz.-Nagy asserts that a Hilbert space contraction operator $T$ can be dilated to a unitary $\cU$. A more general multivariable setting for these ideas is the setup where (i) the unit disk is replaced by a domain…
In this paper we introduce a new technique to prove the existence of closed subspaces of maximal dimension inside sets of topological vector sequence spaces. The results we prove cover some sequence spaces not studied before in the context…
We answer the question of W.T. Gowers, giving an example of a bounded operator on a subspace of Gowers unconditional space which is not a strictly singular perturbation of a restriction of a diagonal operator. We make some observations on…
We present a Banach space $\mathfrak X$ with a Schauder basis of length $\omega\_1$ which is saturated by copies of $c\_0$ and such that for every closed decomposition of a closed subspace $X=X\_0\oplus X\_1$, either $X\_0$ or $X\_1$ has to…
We study maximal regularity with respect to continuous functions for strongly continuous semigroups on locally convex spaces as well as its relation to the notion of admissible operators. This extends several results for classical strongly…
For linear evolution control system described by $\dot{x}=Ax(t)+Bu(t),x(0)=x_{0}$ ($A$ generates a strongly continuous semigroup ${S(t)}_{t\ge 0}$ in a Banach space $X$; $B$ is a linear unbounded operator), the attainable set $K(t)$ is…
The paper is largely concerned with the possibility of obtaining a series representation for a compact linear map $T$ acting between Banach spaces. It is known that, using the notions of $j-$eigenfunctions and $j-$% eigenvalues, such a…
We provide a sufficient condition for an operator $T$ on a non-metrizable and sequentially separable topological vector space $X$ to be sequentially hypercyclic. This condition is applied to some particular examples, namely, a composition…
Given a dynamical system $(X,T)$ and a family $\mathsf{I}\subseteq \mathcal{P}(\omega)$ of "small" sets of nonnegative integers, a point $x \in X$ is said to be $\mathsf{I}$-strong universal if for each $y \in X$ there exists a subsequence…
We construct a family of separable Hilbertian operator spaces, such that the relation of complete isomorphism between the subspaces of each member of this family is complete $\ks$. We also investigate some interesting properties of…
Let $X$ and $Y$ be separable Banach spaces and $T:X\to Y$ be a bounded linear operator. We characterize the non-separability of $T^*(Y^*)$ by means of fixing properties of the operator $T$.
We investigate dynamical properties such as topological transitivity, (sequential) hypercyclicity, and chaos for backward shift operators associated to a Schauder basis on LF-spaces. As an application, we characterize these dynamical…
We investigate discrete-time dynamical systems generated by an infinite-dimensional non-linear operator that maps the Banach space $l_1$ to itself. It is demonstrated that this operator possesses up to seven fixed points. By leveraging the…
The aim of this paper is to present a unified theory of many Kato type representation theorems in terms of solvable forms on Hilbert spaces. In particular, for some sesquilinear forms $\Omega$ on a dense domain $\mathcal{D}$ one looks for…
We prove that if T is a strictly singular 1-1 operator defined on an infinite dimensional Banach space X, then for every infinite dimensional subspace Y of X there exists an infinite dimensional subspace Z of Y such that Z contains orbits…
We study the linear dynamics of the random sequence $(T_n(.))_{n \geq 1}$ of the operators $T_n(\omega) = T(\tau^{n-1}\omega) \dotsm T(\tau \omega) T(\omega), n \geq 1$. These products depend on an ergodic measure-preserving transformation…
We give orthonormal characterizations of collectively compact (limited) sets of linear operators from a Hilbert space to a Banach space.
We study hypercyclicity, Devaney chaos, topological mixing properties and strong mixing in the measure-theoretic sense for operators on topological vector spaces with invariant sets. More precisely, our purpose is to establish links between…
We study non-autonomous observation systems \begin{align*} \dot{x}(t) = A(t) x(t),\quad y(t) = C(t) x(t),\quad x(0) = x_0\in X, \end{align*} where $(A(t))$ is a strongly measurable family of closed operators on a Banach space $X$ and…
Given a category of objects, it is both useful and important to know if all the objects in the category may be realised as sub-objects -- via morphisms in the given category -- of a single object in that category enjoying some nice…