Related papers: Weak Commutativity Between Two Isomorphic Polycycl…

Let the pair of operators, $(H, T)$, satisfy the weak Weyl relation: $Te^{-itH} = e^{-itH}(T + t)$, where $H$ is self-adjoint and $T$ is closed symmetric. Suppose that g is a realvalued Lebesgue measurable function on $\RR$ such that $g \in…

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 $x\in \B$…

A finite group $G$ is called $\psi$-divisible if $\psi(H)|\psi(G)$ for any subgroup $H$ of $G$, where $\psi(H)$ and $\psi(G)$ are the sum of element orders of $H$ and $G$, respectively. In this paper, we extend a result provided in [10], by…

For spaces of analytic functions defined on an open set in $\mathbb{C}^n$ that satisfy certain nice properties, we show that operators that preserve shift-cyclic functions are necessarily weighted composition operators. Examples of spaces…

The first author and Oguni introduced a class of groups of non-positive curvature, called coarsely convex group. The recent success of the theory of groups which are hyperbolic relative to a collection of subgroups has motivated the study…

Given groupoids $\mathscr G$ and $\mathscr H$ as well as an isomorphism $\Psi:\text{Sd}\,\mathscr G\cong\text{Sd}\,\mathscr H$ between subdivisions, we construct an isomorphism $P:\mathscr G\cong\mathscr H$. If $\Psi$ equals $\text{Sd} F$…

In this article we will see some properties that guarantee that a product of an ergodic non-singular action and a probability preserving ergodic action is also an ergodic action. We will start by proving 'The multiplier theorem' for locally…

We give a sufficient condition for two operators to be disjointly frequently hypercyclic. We apply this criterion to composition operators acting on $H(\mathbb D)$ or on the Hardy space $H^2(\mathbb D)$. We simplify a result on disjoint…

A closed subspace is invariant under the Ces\`aro operator $\mathcal{C}$ on the classical Hardy space $H^2(\mathbb D)$ if and only if its orthogonal complement is invariant under the $C_0$-semigroup of composition operators induced by the…

A finite group is said to be weakly separable if every algebraic isomorphism between two $S$-rings over this group is induced by a combinatorial isomorphism. In the paper we prove that every abelian weakly separable group belongs to one of…

This paper discusses the existence of a sufficient condition for an operator to be weakly hypercyclic. We establish a weak hypercyclicity criterion, and thereupon we can answer questions 5.3 and 5.8 posed by Chan and Sanders in 2004.…

The Hardy Inequality (HI) for potentials with countably many singularities of the form $V=\sum_{k\in \mathbf{Z}}\frac{1}{|x-a_k|^2}$ is not a trivial issue. In principle, the more singular poles are, the less the Hardy constant is: it is…

Let $G$ be a finite group and $H$ be a subgroup of $G$. Then $H$ is called a weakly $S\Phi$-supplemented subgroup of $G$, if there exists a subgroup $T$ of $G$ such that $G =HT$ and $H \cap T \leq \Phi (H) H_{sG}$, where $H_{sG}$ denotes…

Let $G$ be a discrete group and let $\mathcal A$ and $\mathcal B$ be two subgroups of $G$-valued continuous functions defined on two $0$-dimensional compact spaces $X$ and $Y$. A group isomorphism $H$ defined between $\mathcal A$ and…

Let $H$ be a complex Hilbert space of dimension not less than $3$ and let ${\mathcal C}$ be a conjugacy class of compact self-adjoint operators on $H$. Suppose that the dimension of the kernels of operators from ${\mathcal C}$ not less than…

This paper deals with representing in concrete fashion those Hilbert spaces that are vector subspaces of the Hardy spaces $H^p(\bb D^n) \ (1\le p\le \infty)$ that remain invariant under the action of coordinate wise multiplication by an…

We study operator algebraic and function theoretic aspects of algebras of bounded nc functions on subvarieties of the nc domain determined by all levels of the unit ball of an operator space (nc operator balls). Our main result is the…

To construct more homogeneous operators, B. Bagchi and G. Misra in \cite{d} introduced the operator $\left(\begin{smallmatrix} T_0 & T_0-T_1 \\ 0 & T_1\\ \end{smallmatrix}\right)$ and proved that when $T_0$ and $T_1$ are homogeneous…

In this paper, we give a brief review concerning diskcyclic operators and then we provide some further characterizations of diskcyclic operators on separable Hilbert spaces. In particular, we show that if $x\in {\mathcal H}$ has a disk…

A finite group is called $\psi$-divisible iff $\psi(H)|\psi(G)$ for any subgroup $H$ of a finite group $G$. Here, $\psi(G)$ is the sum of element orders of $G$. For now, the only known examples of such groups are the cyclic ones of…