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The spectral theorem
for unbounded normal operators
S. J. Bernau |
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Vol. 19 (1966), No. 3, 391–406
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Abstract |
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This paper gives a direct constructive proof of the spectral theorem for a normal operator T (bounded or unbounded) in a complex Hilbert space. It depends on the results, recently obtained by elementary methods, that an unbounded positive self adjoint operator A has a unique positive self adjoint square root A1∕2; and an arbitrary self adjoint operator A has a unique representation A = A+ − A− with A+ and A− self adjoint and positive and the range of each contained in the null space of the other. |
Mathematical Subject Classification
Primary: 46.30
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Milestones
Received: 4 November 1965
Published: 1 December 1966
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Authors |
| S. J. Bernau | |
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