Related papers: Strong transitivity properties for operators

A group action is said to be highly-transitive if it is $k$-transitive for every $k \ge 1$. The main result of this thesis is the following: Main Theorem: The fundamental group of a closed, orientable surface of genus > 1 admits a…

In this paper, we characterize operator-theoretic properties (boundedness, compactness, and Schatten class membership) of Toeplitz operators with positive measure symbols on weighted Fock-Sobolev spaces of fractional order.

Given a uniform space $(X, \mathcal{U})$, we denote by $\mathcal{F}(X)$ to the family of all normal upper semicontinuous fuzzy sets $u \colon X \to [0,1]$ with compact support. In this paper, we study transitivity on some uniformities on…

Distributive subsets of the group of all invertible continuous binary operations on a topological space are considered, and it is proved that the subgroups generated by them are also distributive. A criterion for the distributivity of a…

Let $\mathcal M$ be a factor von Neumann algebra with separable predual and let $T\in \mathcal M$. We call $T$ an irreducible operator (relative to $\mathcal M$) if $W^*(T)$ is an irreducible subfactor of $\mathcal M$, i.e., $W^*(T)'\cap…

Given a Furstenberg family F and a subset {\Gamma} of C, we introduce and explore the notions of F_{\Gamma}-hypercyclic operator and F-hypercyclic scalar set. First, the study of F_C-hypercyclic operators yields new interesting information…

The composition of the Fourier transform in $\mathbb{R}^n$ with a suitable pseudodifferential operator is called a Fourier operator. It is compact in appropriate function spaces. The paper deals with its spectral theory. This is based on…

Hyperspaces form a powerful tool in some branches of mathematics: lots of fractal and other geometric objects can be viewed as fixed points of some functions in suitable hyperspaces - as well as interesting classes of formal languages in…

We provide a sufficient condition for an operator $T$ on a non-metrizable and sequentially separable topological vector space $X$ to be sequentially hypercyclic. This condition is applied to some particular examples, namely, a composition…

A family $f_1,...,f_n$ of operators on a complete metric space $X$ is called contractive if there exists a positive $\lambda < 1$ such that for any $x,y$ in $X$ we have $d(f_i(x),f_i(y)) \leq \lambda d(x,y)$ for some $i$. Austin conjectured…

We consider weakly closed transitive algebras of operators containing non-zero compact operators in real Banach spaces (Lomonosov algebras). It is shown that they are naturally divided in three classes: the algebras of real, complex and…

Functors with an instance of the Traversable type class can be thought of as data structures which permit a traversal of their elements. This has been made precise by the correspondence between traversable functors and finitary containers…

Toeplitz operators (also called localization operators) are a generalization of the well-known anti-Wick pseudodifferential operators studied by Berezin and Shubin. When a Toeplitz operator is positive semi-definite and has trace one we…

For each finite classical group $G$, we classify the subgroups of $G$ which act transitively on a $G$-invariant set of subspaces of the natural module, where the subspaces are either totally isotropic or nondegenerate. Our proof uses the…

Let $X$ be a complex topological vector space with dim$(X)>1$ and $\mathcal{B}(X)$ the space of all continuous linear operators on $X$. In this paper, we extend the concept of supercyclicity of a single operators and strongly continuous…

We say that a sequence of operators $(T_n)$ possesses hereditarily hypercyclic subspaces along a sequence $(n_k)$ if for any subsequence $(m_k)\subset(n_k)$, the sequence $(T_{m_k})$ possesses a hypercyclic subspace. While so far no…

An operator algebra $\mathcal{A}$ acting on a Hilbert space is said to have the closability property if every densely defined linear transformation commuting with $\mathcal{A}$ is closable. In this paper we study the closability property of…

To a pair of subspaces wandering with respect to a row isometry we associate a transfer function which in general is multi-Toeplitz and in interesting special cases is multi-analytic. Then we describe in an expository way how characteristic…

Consider $\mathscr{F}$ a non-empty set of subsets of $\mathbb{N}$. An operator $T$ on $X$ satisfies property $\mathcal{P}_{\mathscr{F}}$ if for any $U$ non-empty open set in $X$, there exists $x\in X$ such that $\{n\in\mathbb{N}: T^nx\in…

For every group $G$, we show that either $G$ has a topologically transitive action on the line $\mathbb R$ by orientation-preserving homeomorphisms, or every orientation-preserving action of $G$ on $\mathbb R$ has a wandering interval.…