Syndetically Hypercyclic Operators |
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Authors: | Alfredo Peris Luis Saldivia |
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Institution: | (1) E.T.S. Arquitectura, Departament de Matemàtica Aplicada, Universitat Politècnica de València, E-46022 València, Spain;(2) Mathematics Department, Michigan State University, East Lansing, MI, 48823, U.S.A |
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Abstract: | Given a continuous linear operator T L(x) defined on a separable
-space X, we will show that T satisfies the Hypercyclicity Criterion if and only if for any strictly increasing sequence of positive integers
such that
the sequence
is hypercyclic. In contrast we will also prove that, for any hypercyclic vector x X of T, there exists a strictly increasing sequence
such that
and
is somewhere dense, but not dense in X. That is, T and
do not share the same hypercyclic vectors. |
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Keywords: | Primary 47A16 Secondary 37D45 46A04 |
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