Hypercyclicity in omega

Author:
Henrik Petersson

Journal:
Proc. Amer. Math. Soc. **135** (2007), 1145-1149

MSC (2000):
Primary 47A16

Published electronically:
October 4, 2006

MathSciNet review:
2262918

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Abstract | References | Similar Articles | Additional Information

Abstract: A sequence of operators is said to be hypercyclic if there exists a vector , called hypercyclic for , such that is dense. A hypercyclic subspace for is a closed infinite-dimensional subspace of, except for zero, hypercyclic vectors. We prove that if is a sequence of operators on that has a hypercyclic subspace, then there exist (i) a sequence of one variable polynomials such that is hypercyclic for every fixed and (ii) an operator that maps nonzero vectors onto hypercyclic vectors for .

We complement earlier work of several authors.

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Additional Information

**Henrik Petersson**

Affiliation:
School of Mathematical Sciences, Chalmers/Göteborg University, SE-412 96 Göteborg, Sweden

Email:
henripet@math.chalmers.se

DOI:
https://doi.org/10.1090/S0002-9939-06-08584-4

Keywords:
Hypercyclic subspace,
omega,
backward shift.

Received by editor(s):
November 11, 2005

Published electronically:
October 4, 2006

Additional Notes:
This work was supported by the The Royal Swedish Academy of Sciences.

Communicated by:
Joseph A. Ball

Article copyright:
© Copyright 2006
American Mathematical Society