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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Noncyclic vectors for $ S\sp{\ast} $


Authors: D. A. Herrero and M. J. Sherman
Journal: Proc. Amer. Math. Soc. 48 (1975), 193-196
MSC: Primary 47A65
DOI: https://doi.org/10.1090/S0002-9939-1975-0374962-0
MathSciNet review: 0374962
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Abstract: It is shown that the linear manifold of $ {H^2}$ consisting of all noncyclic vectors of the backward shift operator $ {S^ \ast }$ is not a countable union of operator ranges.


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DOI: https://doi.org/10.1090/S0002-9939-1975-0374962-0
Keywords: Invariant subspaces, inner functions, backward shift operator
Article copyright: © Copyright 1975 American Mathematical Society