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

Author(s): Aharon Atzmon
Journal: Proc. Amer. Math. Soc. 129 (2001), 1963-1967.
MSC (2000): Primary 47B37; Secondary 46J20
Posted: November 22, 2000
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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: 10.1090/S0002-9939-00-05759-2
PII: S 0002-9939(00)05759-2
Received by editor(s): September 10, 1998
Received by editor(s) in revised form: October 13, 1999
Posted: November 22, 2000
Communicated by: David R. Larson
Copyright of article: Copyright 2000, American Mathematical Society

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