Related papers: Hypercyclic operators, Gauss measures and Polish d…
Recent research has shown that the properties of overcomplete Gabor frames and frames arising from shift-invariant systems form a precise match with certain conditions that are necessary for a frame in $L^2(\mathbf R)$ to have a…
Recently, two new topological properties for operators acting on a topological vector space were introduced: strong hypercyclicity and hypermixing. We introduce a new property called ultra hypercyclicity and compare it to strong…
We give a simple, straightforward proof of the non-hypercyclicity of an arbitrary (bounded or not) normal operator $A$ in a complex Hilbert space as well as of the collection $\left\{e^{tA}\right\}_{t\ge 0}$ of its exponentials, which,…
Let H be a complex Hilbert space, B(H) and S(H) be the spaces of all bounded operators and all self-adjoint operators on H, respectively. We give the concrete forms of the maps on B(H) and also S(H) which preserve the spectrum of certain…
We treat some questions related to supercyclicity of continuous linear operators when acting in locally convex spaces. We extend results of Ansari and Bourdon and consider doubly power bounded operators in this general setting. Some…
For $\mathbb{B}^n$ the $n$-dimensional unit ball and $D_n$ its Siegel unbounded realization, we consider Toeplitz operators acting on weighted Bergman spaces with symbols invariant under the actions of the maximal Abelian subgroups of…
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…
Motivated by the recent developments of pseudo-Hermitian quantum mechanics, we analyze the structure generated by unbounded metric operators in a Hilbert space. To that effect, we consider the notions of similarity and quasi-similarity…
In this paper, we characterize complementable operators and provide more precise expressions for the Schur complement of these operators using a single Douglas solution. We demonstrate the existence of subspaces where the given operator is…
Given a dynamical system, we study the so-called space of shift functions thus introducing another vision on bifurcations and chaos. As an application of the obtained results, we give a partial solution to an open problem formulated in…
We find some sufficient conditions for a system of partial derivatives of an entire function to be complete in the space $H(\mathbb{C}^d)$ of all entire functions of $d$ variables. As an appliation of this result we describe new classes of…
We formulate a geometric measurement theory of dynamical classical systems possessing both continuous and discrete degrees of freedom. The approach is covariant with respect to choices of clocks and canonically incorporates laboratories.…
We derive rates of convergence for the mixing of operators under infinitely divisible measures in the framework of linear dynamics on Banach spaces. Our approach is based on the characterization of mixing in terms of codifference…
We study hypercyclicity of the Toeplitz operators in the Hardy space $H^2(\mathbb{D})$ with symbols of the form $p(\bar{z}) +\phi(z)$, where $p$ is a polynomial and $\phi \in H^\infty(\mathbb{D})$. We find both necessary and sufficient…
In this paper, we prove that if $T$ is diskcyclic operator then the closed unit disk multiplied by the union of the numerical range of all iterations of $T$ is dense in $\mathcal H$. Also, if $T$ is diskcyclic operator and $|\lambda|\le 1$,…
Returning to a classical question in Harmonic Analysis we strengthen an old result of Walter Rudin. We show that there exists a weakly almost periodic function on the group of integers Z which is not in the norm-closure of the algebra B(Z)…
We characterize the semigroups of composition operators that are strongly continuous on the mixed norm spaces $H(p,q,\alpha)$. First, we study the separable spaces $H(p,q,\alpha)$ with $q<\infty,$ that behave as the Hardy and Bergman…
We prove the spaceability of the set of hypercyclic vectors for {\em shifts-like operators}. Shift-like operators appear naturally as composition operators on $L^p(X)$, when the underlying space $X$ is dissipative. In the process of proving…
We consider operators acting on a Hilbert space that can be written as the sum of a shift and a diagonal operator and determine when the operator is hyponormal. The condition is presented in terms of the norm of an explicit block Jacobi…
Linear spaces with an Euclidean metric are ubiquitous in mathematics, arising both from quadratic forms and inner products. Operators on such spaces also occur naturally. In recent years, the study of multivariate operator theory has made…