Related papers: Existence of common and upper frequently hypercycl…
Given $\mathcal{A}$ the family of weights $a=(a_n)_n$ decreasing to $0$ such that the series $\sum_{n=0}^{\infty} a_n$ diverges, we show that the supremum on $\mathcal{A}$ of lower weighted densities coincides with the unweighted upper…
We study the existence of hypercyclic algebras for convolution operators $\Phi(D)$ on the space of entire functions whose symbol $\Phi$ has unimodular constant term. In particular, we provide new eigenvalue criteria for the existence of…
There has been a long-standing conjecture in Banach algebra that every amenable operator is similar to a normal operator. In this paper, we study the structure of amenable operators on Hilbert spaces. At first, we show that the conjecture…
It is well known that subspaces of the Hardy space over the unit disk which are invariant under the backward shift occur as the image of an observability operator associated with a discrete-time linear system with stable state-dynamics, as…
We study shadowing and chain recurrence in the context of linear operators acting on Banach spaces or even on normed vector spaces. We show that for linear operators there is only one chain recurrent set, and this set is actually a closed…
Let us denote ${\cal V}$, the finite dimensional vector spaces of functions of the form $\psi(x) = p_n(x) + f(x) p_m(x)$ where $p_n(x)$ and $p_m(x)$ are arbitrary polynomials of degree at most $n$ and $m$ in the variable $x$ while $f(x)$…
We provide conditions for a linear map of the form $C_{R,T}(S)=RST$ to be $q$-frequently hypercyclic on algebras of operators on separable Banach spaces. In particular, if $R$ is a bounded operator satisfying the $q$-Frequent Hypercyclicity…
We prove that a large class of trace-class perturbations of diagonalizable normal operators on a separable, infinite dimensional complex Hilbert space have non-trivial closed hyperinvariant subspaces. Moreover, a large subclass consists of…
We construct a generalization of the theory of symmetric functions involving functions of commuting and anticommuting (Grassmannian) variables. These new functions, called symmetric functions in superspace, are invariant under the diagonal…
Operators of multiplication by independent variables on the space of square summable functions over the torus and its Hardy subspace are considered. Invariant subspaces where the operators are compatible are described.
We study the cyclic and supercyclic dynamical properties of weighted composition operators on the Fock space $\mathcal{F}_2$. A complete characterization of cyclicity which depends on the derivative of the symbol for the composition…
Consider the Dirichlet-type space on the bidisk consisting of holomorphic functions $f(z_1,z_2):=\sum_{k,l\geq 0}a_{kl}z_1^kz_2^l$ such that $\sum_{k,l\geq 0}(k+1)^{\alpha_1} (l+1)^{\alpha_2}|a_{kl}|^2 <\infty.$ Here the parameters…
In this paper, we study frequent hypercyclicity for strongly continuous semigroups of operators $\left\{T_{t}\right\}_{t\in\Delta}$ indexed with complex sectors. We propose a revised and more natural definition of frequent hypercyclicity…
We provide a criterion for $\varepsilon$-hypercyclicity. Also, we extend the ideas of Badea, Grivaux, M\"uller and Bayart to construct $\varepsilon$-hypercyclic operators which are not hypercyclic in a wider class of separable Banach…
We give an affirmative answer to a question asked by Faghih-Ahmadi and Hedayatian regarding supercyclic vectors. We show that if $\mathcal X$ is an infinite-dimensional normed linear space and $T$ is a supercyclic operator on $\mathcal X$,…
We prove the existence of algebras of hypercyclic vectors in three cases: convolution operators, composition operators, and backward shift operators.
The sets of strongly supercyclic, weakly l-sequentially supercyclic, weakly sequentially supercyclic, and weakly supercyclic vectors for an arbitrary normed-space operator are all dense in the normed space, regardless the notion of…
We study the class of operators $S_{\alpha,\beta}$ obtained by compressing the Hardy shift on the parametric spaces $H^2_{\alpha, \beta}$ corresponding to the pair $\{\alpha,\beta\}$ satisfying $|\alpha|^2+|\beta|^2=1$. We show, for nonzero…
We study finite systems of subspaces of a complex Hilbert space such that each pair of subspaces satisfies a certain condition as described in the following. For each subspace excepting the first one an angle between this subspace and the…
Let (k(n)) n=1,2,... be a strictly increasing sequence of positive integers . We consider a specific sequence of differential operators Tk(n),{\lambda} , n=1,2,... on the space of entire functions , that depend on the sequence (k(n))…