Operators Commuting with the Volterra Operator are not Weakly Supercyclic
نویسندگان
چکیده
منابع مشابه
Operators commuting with the Volterra operator are not weakly supercyclic
We prove that any bounded linear operator on Lp[0, 1] for 1 6 p < ∞, commuting with the Volterra operator V , is not weakly supercyclic, which answers affirmatively a question raised by Léon-Saavedra and Piqueras-Lerena. It is achieved by providing an algebraic flavored condition on an operator which prevents it from being weakly supercyclic and is satisfied for any operator commuting with V . ...
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We prove that on R , there is no n-supercyclic operator with 1 ≤ n < b 2 c i.e. if R has an n-dimensional subspace whose orbit under T ∈ L(R ) is dense in R , then n is greater than b 2 c. Moreover, this value is optimal. We then consider the case of strongly n-supercyclic operators. An operator T ∈ L(R ) is strongly n-supercyclic if R has an ndimensional subspace whose orbit under T is dense i...
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ژورنال
عنوان ژورنال: Integral Equations and Operator Theory
سال: 2010
ISSN: 0378-620X,1420-8989
DOI: 10.1007/s00020-010-1790-y