We prove that l contains a dense set of vectors which are hypercyclic simultaneously for all multiples of the backward shift operator by constants of absolute value greater than 1.

we consider the transitive linear maps on the operator algebra $b(x)$for a separable banach space $x$. we show if a bounded linear map is norm transitive on $b(x)$,then it must be hypercyclic with strong operator topology. also we provide a sot-transitivelinear map without being hypercyclic in the strong operator topology.

We consider the transitive linear maps on the operator algebra $B(X)$for a separable Banach space $X$. We show if a bounded linear map is norm transitive on $B(X)$,then it must be hypercyclic with strong operator topology. Also we provide a SOT-transitivelinear map without being hypercyclic in the strong operator topology.

Let H be a Hilbert space of functions analytic on a plane domain G such that for each λ in G the linear functional of evaluation at λ given by f −→ f(λ) is a bounded linear functional on H . By the Riesz representation theorem there is a vector Kλ in H such that f(λ) =< f,Kλ >. Let T = (T1, T2) be the pair of commutative bounded linear operators T1 and T2 acting on H . Put F = {T1T2 : m,n ≥ 0}....

Even linear operators on infinite-dimensional spaces can display interesting dynamical properties and yield important links among functional analysis, differential and global geometry and dynamical systems, with a wide range of applications. In particular, hypercyclicity is an essentially infinite-dimensional property, when iterations of the operator generate a dense subspace. A Fréchet space a...

We study dynamical notions lying between $$\mathcal{U}$$ -frequent hypercyclicity and reiterative by investigating weighted upper densities the unweighted density Banach density. While chaos implies hypercyclicity, we show that does not imply with respect to any Moreover, if T is -frequently hypercyclic (resp. reiteratively hypercyclic) then n-fold product of still U-frequently this implicatio...