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We show that topological mixing, weak mixing and total transitivity are equivalent for coded systems. We provide an example of a mixing coded system which cannot be approximated by any increasing sequence of mixing shifts of finite type,…

A classical result by R. Rochberg says that every bounded Toeplitz operator $T$ on the Hilbert Paley-Wiener space $\mathrm{PW}_a^2$ admits a bounded symbol $\varphi$. We generalize this result to Toeplitz operators on the Banach…

We give sufficient conditions for the continuity in norm of the translation operator in the Musielak-Orlicz LM spaces. An application to the convergence in norm of approximate identities is given, whereby we prove density results of the…

An action of a group $G$ is highly transitive if $G$ acts transitively on $k$-tuples of distinct points for all $k \geq 1$. Many examples of groups with a rich geometric or dynamical action admit highly transitive actions. We prove that if…

In this current study, the most apparent aspect is to submit a new geometric sequence space. We investigate its topological properties , inclusion relations, Geometric statistical convergence and Geometric property of Orlicz function and .…

Let $\Phi$ be a Young function. We study convolution properties for symbol classes $s_{A,\Phi}$, which consist of all $a$ such that the pseudo-differential operator $\operatorname{Op} _A(a)$ is in the Orlicz Schatten class $\mathscr I _\Phi…

In this paper we provide a full characterization of cyclic composition operators defined on the d-dimensional Fock space $\mathcal F(\mathbb C^d)$ in terms of their symbol. Also, we study the supercyclicity and convex-cyclicity of this type…

We give a sufficient condition for a composition operator with positive characteristic to be compact on the Hardy space of Dirichlet series.

In this paper, we study bounded and closed range multiplication and composition operators between two different Orlicz spaces.

Let $\Phi_1$ and $\Phi_2$ be nondecreasing functions from $\mathbb{R_+}=(0,\infty)$ onto itself. For $i=1,2$ and $\gamma \in \mathbb{R}$, define the Orlicz class $L_{\Phi_{i}}(\mathbb{R_+})$ to be the set of Lebesgue-measurable functions…

Let $G$ be a locally compact group and $\mu$ an admissible probability measure on $G$. Let $(B,\nu)$ be the universal topological Poisson $\mu$-boundary of $(G,\mu)$ and $\Pi_s(G)$ the universal minimal strongly proximal $G$-flow. This note…

On the twisted Fock spaces $ \mathcal{F}^\lambda(\mathbb{C}^{2n}) $ we consider two types of convolution operators $ S_\varphi $ and $ \widetilde{S}_\varphi $ associated to an element $ \varphi \in \mathcal{F}^\lambda(\mathbb{C}^{2n}) .$ We…

Using a result from ergodic Ramsey theory, we answer a question posed by B\`es, Martin, Peris and Shkarin by showing a mixing operator $T$ on a Hilbert space such that the tuple $(T, T^2)$ is not disjoint transitive.

Binary clustering systems are closely related to monotone transit functions. An interesting class are pyramidal transit functions defined by the fact that their transit sets form an interval hypergraph. We investigate here properties of…

Let $H$, $T$ and $C_n$ be a graph, a tree and a cycle of order $n$, respectively. Let $H^{(i)}$ be the complete join of $H$ and an empty graph on $i$ vertices. Then the Cartesian product $H\Box T$ of $H$ and $T$ can be obtained by applying…

In the paper we find representation of the space of pointwise multipliers between two Orlicz function spaces, which appears to be another Orlicz space and the formula for the Young function generating this space is given. Further, we apply…

Let $S_n f$ be the $n$th partial sum of the Fourier series of a function $f$ in $L^1(\D)$, where $\D$ is the ring of integers of a local field $K$. For $1<p<\infty$, we characterize all weight functions $w$ so that the partial sum operators…

In this paper we characterize Li-Yorke chaotic composition operators on Orlicz spaces. Indeed some necessary and suffcient conditions are provided for Li-Yorke chaotic composition operator C' on the Orlicz space Lp. In some cases we have…

We study when a continuous isometric action of a Polish group on a complete metric space is, or can be, transitive. Our main results consist of showing that certain Polish groups, namely $\mathrm{Aut}^*(\mu)$ and $\mathrm{Homeo}^+[0,1]$,…

A sequence $\{T_n\}_{n=1}^{\infty}$ of bounded linear operators between separable Banach spaces $X, Y$ is called diskcyclic if there exists a vector $x\in X$ such that the disk-scaled orbit $\{\alpha T_n x: n\in \mathbb{N}, \alpha…