منابع مشابه
Common Hypercyclic Vectors for Families of Operators
We provide a criterion for the existence of a residual set of common hypercyclic vectors for an uncountable family of hypercyclic operators, which is based on a previous one given by Costakis and Sambarino. As an application, we get common hypercyclic vectors for a particular family of hypercyclic scalar multiples of the adjoint of a multiplier in the Hardy space, generalizing recent results by...
متن کاملCommon Hypercyclic Vectors for Multiples of Backward Shift
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.
متن کاملCommon Hypercyclic Vectors for Composition Operators
A continuous operator acting on a topological vector space X is called hypercyclic provided there exists a vector x ∈ X such that its orbit {T nx; n ≥ 1} is dense in X. Such a vector is called a hypercyclic vector for T . The set of hypercyclic vectors will be denoted by HC(T ). The first example of hypercyclic operator was given by Birkhoff, 1929 [3], who shows that the operator of translation...
متن کاملHypercyclic Operators That Commute with the Bergman Backward Shift
The backward shift B on the Bergman space of the unit disc is known to be hypercyclic (meaning: it has a dense orbit). Here we ask: “Which operators that commute with B inherit its hypercyclicity?” We show that the problem reduces to the study of operators of the form φ(B) where φ is a holomorphic self-map of the unit disc that multiplies the Dirichlet space into itself, and that the question o...
متن کاملOperators with Common Hypercyclic Subspaces
We provide a reasonable sufficient condition for a family of operators to have a common hypercyclic subspace. We also extend a result of the third author and A. Montes [22], thereby obtaining a common hypercyclic subspace for certain countable families of compact perturbations of operators of norm no larger than one.
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ژورنال
عنوان ژورنال: Journal of Operator Theory
سال: 2017
ISSN: 0379-4024,1841-7744
DOI: 10.7900/jot.2015jun13.2106