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Invariant subspaces of operators related to the unilateral shift

Published online by Cambridge University Press:  09 April 2009

S. R. Caradus
S. R. Caradus
Affiliation:
Queen's University at KingstonDepartment of Mathematics Ontario, Canada
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Among all non-self-adjoint operators, the shift has a special place in questions relating to invariant subspaces. It is therefore natural to attempt to use this fact to study other operators related in some way to the shift. Examples of this procedure are available in the work of Freeman [3] and Lim [5] where perturbations of the shift are studied.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 16 , Issue 2 , September 1973 , pp. 210 - 213
Copyright
Copyright © Australian Mathematical Society 1973

References

[1]Beurling, A., ‘On two peoblems concerning linear transformations in Hilbert sapce’, Acta Math., 81 (1949), 239–255.CrossRefGoogle Scholar
[2]Caradus, S. R., ‘Universal operators and invariant subspaces’, Proc. Amer. Math. Soc. 23 (1969), 526–527.CrossRefGoogle Scholar
[3]Freeman, J. M., ‘Perturbations of the shift opeartor’, Trans. Amer. Math. Soc. 114 (1965), 251–260.CrossRefGoogle Scholar
[4]Gohberg, I. C. and Krein, M. G., Introduction to the theory of linear non self adjoint opeartors (Translations of Mathematical Monographs, Vol. 18, Amer. Math. Soc., (1969).Google Scholar
[5]Lin, S. C., ‘Perturbations of the unilateral shift’, Bull. Amer. Math. Soc. 77 (1971), 621–624.CrossRefGoogle Scholar
[6]Sz-Nagy, B. and Foias, C., ‘Vecteurs cycliques et quasi-affinités’ Studia Math. 31 (1968), 35–42.CrossRefGoogle Scholar
[7]Sz-Nagy, B. and Foias, C., Harmoinc Analysis of Operators on Hilbert Space (North-Holland, American Elsevier, 1970).Google Scholar