Somewhere Dense Orbits are Everywhere Dense

Let T be a continuous linear operator on a locally convex topological vector space X. We show that if x ∈ X has orbit under T that is somewhere dense in X, then the orbit of x under T must be everywhere dense in X, answering a question raised by Alfredo Peris.

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Bibliographic Details
Published in:Indiana University mathematics journal 2003-01, Vol.52 (3), p.811-819
Main Authors: Bourdon, Paul S., Feldman, Nathan S.
Format: Article
Language:English
Subjects:
Cyclic vectors
Eigenvalues
Exact sciences and technology
Hilbert spaces
Integers
Linear transformations
Mathematical analysis
Mathematical theorems
Mathematical vectors
Mathematics
Operator theory
Polynomials
Scalars
Sciences and techniques of general use
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Description
Summary:Let T be a continuous linear operator on a locally convex topological vector space X. We show that if x ∈ X has orbit under T that is somewhere dense in X, then the orbit of x under T must be everywhere dense in X, answering a question raised by Alfredo Peris.
ISSN:0022-2518
1943-5258
DOI:10.1512/iumj.2003.52.2303