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 کاملBanach Spaces
(A revised and expanded version of these notes are now published by Springer.) 1 Banach Spaces Definition A normed vector space X is a vector space over R or C with a function called the norm. 1. The set of real numbers with the norm taken to be the absolute value.
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ژورنال
عنوان ژورنال: Michigan Mathematical Journal
سال: 1996
ISSN: 0026-2285
DOI: 10.1307/mmj/1029005536