Vol. 19, No. 3, 1966

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The spectral theorem for unbounded normal operators

S. J. Bernau

Vol. 19 (1966), No. 3, 391–406

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 A12; 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
Received: 4 November 1965
Published: 1 December 1966
S. J. Bernau