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 . ...
متن کاملn-supercyclic and strongly n-supercyclic operators in finite dimensions
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...
متن کاملSome Properties of N-supercyclic Operators
Let T be a continuous linear operator on a Hausdorff topological vector space X over the field C. We show that if T is N -supercyclic, i.e., if X has an N dimensional subspace whose orbit under T is dense in X , then T ∗ has at most N eigenvalues (counting geometric multiplicity). We then show that N -supercyclicity cannot occur nontrivially in the finite dimensional setting: the orbit of an N ...
متن کاملPower Bounded Operators and Supercyclic Vectors
Abstract. By the well-known result of Brown, Chevreau and Pearcy, every Hilbert space contraction with spectrum containing the unit circle has a nontrivial closed invariant subspace. Equivalently, there is a nonzero vector which is not cyclic. We show that each power bounded operator on a Hilbert space with spectral radius equal to one has a nonzero vector which is not supercyclic. Equivalently...
متن کاملPower Bounded Operators and Supercyclic Vectors Ii
We show that each power bounded operator with spectral radius equal to one on a reflexive Banach space has a nonzero vector which is not supercyclic. Equivalently, the operator has a nontrivial closed invariant homogeneous subset. Moreover, the operator has a nontrivial closed invariant cone if 1 belongs to its spectrum. This generalizes the corresponding results for Hilbert space operators. Fo...
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2004
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2003.11.049