Pathological hypercyclic operators |
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Authors: | Héctor N Salas |
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Institution: | (1) Department of Mathematics, University of Puerto Rico, Mayagüez, 00681, Puerto Rico |
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Abstract: | We exhibit a hypercyclic operator whose square is not hypercyclic. Our operator is necessarily unbounded since a result of
S. Ansari asserts that powers of a hypercyclic bounded operator are also hypercyclic. We also exhibit an unbounded Hilbert
space operator whose non-zero vectors are hypercyclic.
Received: 19 March 2005; revised: 18 July 2005 |
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Keywords: | Primary 47A16 Secondary 47B99 |
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