منابع مشابه
Small sets and hypercyclic vectors
We study the “smallness” of the set of non-hypercyclic vectors for some classical hypercyclic operators.
متن کاملCommon 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 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 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 کاملProlongations and cyclic vectors
For functions belonging to invariant subspaces of the backward shift operator Bf = (f f(0))/z on spaces of analytic functions on the unit disk D, we explore, in a systematic way, the continuation properties of these functions.
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ژورنال
عنوان ژورنال: Journal of Functional Analysis
سال: 1995
ISSN: 0022-1236
DOI: 10.1006/jfan.1995.1036