Tensor products of recurrent hypercyclic semigroups
نویسنده
چکیده
We study tensor products of strongly continuous semigroups on Banach spaces that satisfy the hypercyclicity criterion, the recurrent hypercyclicity criterion or are chaotic.
منابع مشابه
Hypercyclic Behaviour of Operators in a Hypercyclic C0-Semigroup
Let {Tt}t≥0 be a hypercyclic strongly continuous semigroup of operators. Then each Tt (t > 0) is hypercyclic as a single operator, and it shares the set of hypercyclic vectors with the semigroup. This answers in the affirmative a natural question concerning hypercyclic C0-semigroups. The analogous result for frequent hypercyclicity is also obtained.
متن کاملExistence and Nonexistence of Hypercyclic Semigroups
In these notes we provide a new proof of the existence of a hypercyclic uniformly continuous semigroup of operators on any separable infinitedimensional Banach space that is very different from—and considerably shorter than—the one recently given by Bermúdez, Bonilla and Martinón. We also show the existence of a strongly dense family of topologically mixing operators on every separable infinite...
متن کاملFunction spaces of Rees matrix semigroups
We characterize function spaces of Rees matrixsemigroups. Then we study these spaces by using the topologicaltensor product technique.
متن کاملExistence theorems in linear chaos
Chaotic linear dynamics deals primarily with various topological ergodic properties of semigroups of continuous linear operators acting on a topological vector space. We treat the questions of the following type. Characterize which of the spaces from a given class support a semigroup of prescribed shape satisfying a given topological ergodic property. In particular, we characterize LBS-spaces (...
متن کاملA review of some recent work on hypercyclicity
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...
متن کامل