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Proceedings of the American Mathematical Society

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Invariant subspaces of arbitrary multiplicity for the shift on $\ell^1$


Author: Aharon Atzmon
Journal: Proc. Amer. Math. Soc. 129 (2001), 1963-1967
MSC (2000): Primary 47B37; Secondary 46J20
DOI: https://doi.org/10.1090/S0002-9939-00-05759-2
Published electronically: November 22, 2000
MathSciNet review: 1002583
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Abstract:

It is shown that if $n$ is a positive integer or $n=\infty$, then the unilateral shift on $\ell^1$ has an invariant subspace such that its restriction to it has multiplicity $n$.


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Additional Information

Aharon Atzmon
Affiliation: School of Mathematical Sciences, Tel Aviv University, Tel Aviv 69978, Israel
Email: aatzmon@math.tau.ac.il

DOI: https://doi.org/10.1090/S0002-9939-00-05759-2
Received by editor(s): September 10, 1998
Received by editor(s) in revised form: October 13, 1999
Published electronically: November 22, 2000
Communicated by: David R. Larson
Article copyright: © Copyright 2000 American Mathematical Society