Abstract
We consider families of increasing ∗ ^\ast -invariant subspaces of H 2 ( D ) {H^2}(D) , and from these we construct canonical isometrics from certain L 2 {L^2} spaces to H 2 {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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