A hypercyclicity criterion with applications
نویسندگان
چکیده
منابع مشابه
Hypercyclicity Criterion of Multiple Weighted Composition Operators
In this paper we give some sufficient conditions for the adjoint of the multiple weighted composition operators acting on some function spaces satisfying the Hypercyclicity Criterion. Mathematics Subject Classification: 47B37; 47B33
متن کاملTopological Mixing and Hypercyclicity Criterion for Sequences of Operators
For a sequence {Tn} of continuous linear operators on a separable Fréchet space X, we discuss necessary conditions and sufficient conditions for {Tn} to be topologically mixing, and the relations between topological mixing and the Hypercyclicity Criterion. Among them are: 1) topological mixing is equivalent to being hereditarily densely hypercyclic; 2) the Hypercyclicity Criterion with respect ...
متن کاملA Criterion for Closed Immersions and Applications
Example 1.1. Let C ⊆ Ak be the nodal cubic plane curve given by y 2 = x + x, where k is some algebraically closed field. Let C̃ be its normalization; then C̃ ∼= A. Finally, let D be the open subcurve of C̃ obtained by removing one of the two points lying over the node of C. We consider the morphism D → Ak. Via an explicit parametric form, it is easy to check that this morphism is injective both on...
متن کاملJ-class Operators and Hypercyclicity
The purpose of the present work is to treat a new notion related to linear dynamics, which can be viewed as a “localization” of the notion of hypercyclicity. In particular, let T be a bounded linear operator acting on a Banach space X and let x be a non-zero vector in X such that for every open neighborhood U ⊂ X of x and every non-empty open set V ⊂ X there exists a positive integer n such tha...
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 کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2007
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2006.05.019