Vol. 42, No. 3, 1972

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On a conjecture of L. B. Page

Cedric Felix Schubert

Vol. 42 (1972), No. 3, 733–737

If 𝒦′ is an Hilbert space and a subspace which is invariant under a unilateral shift S on 𝒦 one can ask when a bounded operator T on which commutes with S can be extended to a bounded operator on all of 𝒦 which also commutes with S. Here this problem is considered in the special case that 𝒦 is a Hardy space H2 of functions analytic in the unit-disk with values in a finite dimensional Hilbert space. For this situation an easily derived necessary condition is shown to be sufficient. Further those for which the extension to 𝒦′ is unique are characterized.

Mathematical Subject Classification 2000
Primary: 47A20
Received: 9 August 1971
Published: 1 September 1972
Cedric Felix Schubert