Related papers: Subspace-hypercyclic weighted shifts

The translation of an operator is defined by using conjugation with time-frequency shifts. Thus, one can define $\Lambda$-shift-invariant subspaces of Hilbert-Schmidt operators, finitely generated, with respect to a lattice $\Lambda$ in…

We study the spaceability of the set of recurrent vectors $\text{Rec}(T)$ for an operator $T:X\longrightarrow X$ on a Banach space $X$. In particular: we find sufficient conditions for a quasi-rigid operator to have a recurrent subspace;…

A conditional weighted composition operator $T_u: L^p(\Sigma)\rightarrow L^p(\mathcal{A})$ ($1\leq p<\infty$), is defined by $T_u(f):= E^{\mathcal{A}}(u f\circ \varphi)$, where $\varphi: X\rightarrow X$ is a measurable transformation, $u$…

Let $D$ be the differentiation operator $Df=f'$ acting on the Fr\'echet space $\H$ of all entire functions in one variable with the standard (compact-open) topology. It is known since 1950's that the set $H(D)$ of hypercyclic vectors for…

In a recent paper [15], Hilbert space operators $T$ with the property that each sequence of the form $\{\|T^n h\|^2\}_{n=0}^{\infty}$ is conditionally positive definite in a semigroup sense were introduced. In the present paper, this line…

A bounded linear Hilbert space operator $S$ is said to be a $2$-isometry if the operator $S$ and its adjoint $S^*$ satisfy the relation $S^{*2}S^{2} - 2 S^{*}S + I = 0$. In this paper, we study Hilbert space operators having liftings or…

The weighted shift operators turn out to be extremely useful in supplying interesting examples of operators on Hilbert spaces. With a view to study a continuous analogue of weighted shifts, M. Embry and A. Lambert initiated the study of a…

Let H_0 (resp. H_\infty denote the class of commuting pairs of subnormal operators on Hilbert space (resp. subnormal pairs), and for an integer k>=1 let H_k denote the class of k-hyponormal pairs in H_0. We study the hyponormality and…

We investigate a generalization of weighted shifts where each weight $w_k$ is replaced by an operator $T_k$ going from a Banach space $X_k$ to another one $X_{k-1}$. We then look if the obtained shift operator $B_{(T_k)}$ defined on the…

This article is intended to outline some the recent work by the author on the chaoticity of some specific bakward shift unbounded operators realized as differential operators acting on some Fock-Bargmann spaces and give suficient conditions…

By H\"ormander's $L^2$-m\'ethode, we study some operators in the Hilbert space of weight $L^2(\mathbb{C}, \mathrm{e}^{-|z|^2})$. We prove in each case of operator the existence of its inverse which is also a bounded operator.

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.

For a Hilbert space H included in L^1_{loc} (R) of functions on $R we obtain a representation theorem for the multipliers M commuting with the shift operator S. This generalizes the classical result for multipliers in L^2(R) as well as our…

Let $\eps >0$. We prove that there exists an operator $T_\eps:\ell_2\to\ell_2$, such that for any polynomial $P$ we have $\|{P(T)}\| \leq(1+\eps)\|{P}\|_\infty$, but which is not similar to a contraction, {\it i.e.} there does not exist an…

We explore Hilbert space reformulations of Riemann Hypothesis developed by Nyman, Beurling, B\'{a}ez-Duarte, et. al. with a weighted Bergman space $\mathcal{H}=A_1^2(\mathbb{D})$, i.e., Riemann hypothesis holds if and only if the Hilbert…

Let $\mathcal{W}$ be the corresponding wandering subspace of an invariant subspace of the Bergman shift. By identifying the Bergman space with $H^2(\mathbb{D}^2)\ominus[z-w]$, a sufficient and necessary conditions of a closed subspace of…

In this paper we establish hypercyclicity of continuous linear operators on $H(\mathbb{C})$ that satisfy certain commutation relations.

In this paper, we study the linear dynamical properties of shift operators on some classes of Segal algebras. Moreover, we characterize hypercyclic generalized bilateral shift operators on the standard Hilbert module.

In this paper we show that every bounded linear operator T on a Hilbert space H has a closed non-trivial invariant subspace.

In the following text for cardinal number $\tau>0$, and self--map $\varphi:\tau\to\tau$ we show the generalized shift operator $\sigma_\varphi(\ell^2(\tau))\subseteq\ell^2(\tau)$ (where…