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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Isometries of $ \sp{\ast} $-invariant subspaces


Author: Arthur Lubin
Journal: Trans. Amer. Math. Soc. 190 (1974), 405-415
MSC: Primary 47B37; Secondary 47A15
DOI: https://doi.org/10.1090/S0002-9947-1974-0338823-9
MathSciNet review: 0338823
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Abstract: We consider families of increasing $ ^\ast$-invariant subspaces of $ {H^2}(D)$, and from these we construct canonical isometrics from certain $ {L^2}$ spaces to $ {H^2}$. We give necessary and sufficient conditions for these maps to be unitary, and discuss the relevance to a problem concerning a concrete model theory for a certain class of operators.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1974-0338823-9
Keywords: Invariant subspace, inner function, restricted shift operator, concrete model theory for operators
Article copyright: © Copyright 1974 American Mathematical Society