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Operator-valued inner
functions analytic on the closed disc
Stephen LaVern Campbell |
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Vol. 41 (1972), No. 1, 57–62
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Abstract |
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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
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Milestones
Received: 29 January 1971
Published: 1 April 1972
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Authors |
| Stephen LaVern Campbell | |
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