Related papers: Boundedly Spaced Subsequences and Weak Dynamics

This paper considers weak supercyclicity for bounded linear operators on a normed space. On the one hand, weak supercyclicity is investigated for classes of Hilbert-space operators: (i) self-adjoint operators are not weakly supercyclic,…

This is an expository-survey on weak stability of bounded linear operators acting on normed spaces in general and, in particular, on Hilbert spaces. The paper gives a comprehensive account of the problem of weak operator stability,…

This is an exposition on supercyclicity and weak supercyclicity, especially designed to advance further developments in weakly supercyclicity, which is a recent research field showing significant momentum during the past two decades. For…

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 $x\in \B$…

It is known that weak l-sequential supercyclicity implies weak quasistability, and it is still unknown weather weak l-sequential supercyclicity implies weak stability, much less whether weak supercyclicity implies weak stability (although…

There is no supercyclic power bounded operator of class $C_{1{\textstyle\cdot}}.$ There exist, however, weakly l-sequentially supercyclic unitary operators$.$ We show that if $T$ is a weakly l-sequentially supercyclic power bounded operator…

This paper provides conditions (i) to distinguish weak supercyclicity form supercyclicity for operators acting on normed and Banach spaces, and also (ii) to ensure when weak supercyclicity implies weak stability.

It is known that supercyclicity implies strong stability. It is not known whether weak l-sequential supercyclicity implies weak stability. In this paper we prove that weak l-sequential supercyclicity implies weak quasistability. Corollaries…

We show that (for the weak operator topology) the set of unitary operators on a separable infinite-dimensional Hilbert space is residual in the set of all contractions. The analogous result holds for isometries and the strong operator…

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.…

This paper is concerned with the convergence of power sequences and stability of Hilbert space operators, where "convergence" and "stability" refer to weak, strong and norm topologies. It is proved that an operator has a convergent power…

We discuss the two closely related, but different concepts of weak and almost weak stability for the powers of a contraction on a separable Hilbert space. Extending Halmos' and Rohlin's theorems in ergodic theory as a model, we show that…

We study the asymptotic behaviour of contractive operators and strongly continuous semigroups on separable Hilbert spaces using the notion of rigidity. In particular, we show that a "typical" contraction $T$ contains the unit circle times…

A bounded linear operator T on Hilbert space is subspace-hypercyclic for a subspace M if there exists a vector whose orbit under T intersects the subspace in a relatively dense set. We construct examples to show that subspace-hypercyclicity…

Given a countable dense subset D of an infinite-dimensional separable Hilbert space H the set of operators for which every vector in D except zero is hypercyclic (weakly supercyclic) is residual for the strong (resp. weak) operator topology…

Four possible definitions of the commutation relation $[S,T]=\Id$ of two closable unbounded operators $S,T$ are compared. The {\em weak} sense of this commutator is given in terms of the inner product of the Hilbert space $\H$ where the…

This dissertation summarizes my investigations in operator theory during my PhD studies. The first chapter is an introduction to that field of operator theory which was developed by B. Sz.-Nagy and C. Foias, the theory of power-bounded…

By a bounded backward sequence of the operator $T$ we mean a bounded sequence $\{x_n\}$ satisfying $Tx_{n+1}=x_n$. In \cite{Pa} we have characterized contractions with strongly stable nonunitary part in terms of bounded backward sequences.…

Let D be a self-adjoint differential operator of Dirac type acting on sections in a vector bundle over a closed Riemannian manifold M. Let H be a closed D-invariant subspace of the Hilbert space of square integrable sections. Suppose D…

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;…