Vol. 41, No. 1, 1972

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Operator-valued inner functions analytic on the closed disc

Stephen LaVern Campbell

Vol. 41 (1972), No. 1, 57–62

It is shown that the class of operator valued inner functions analytic on the closed disc is sufficiently large for the invariant subspace problem. These inner functions are then transferred to the upper half-plane and studied via the differential equation U= iAU. The relationship between A and U is investigated. Necessary and sufficient conditions are given on A for U to be the Potapov inner function of a normal operator.

Mathematical Subject Classification 2000
Primary: 47A15
Secondary: 46J15
Received: 29 January 1971
Published: 1 April 1972
Stephen LaVern Campbell