Article

    Ufa Mathematical Journal
    Volume 9, Number 4, pp. 85-96

    Spectral decomposition of a normal operator in a real Hilbert space


    Oreshina M.N.

    DOI:10.13108/2017-9-4-85

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    Unbounded normal operators acting in a real Hilbert space are considered. In this article we carry over the classic results of the spectral theory to the case of such operators. The questions connected with the complexification and decomplexification of normal operators are discussed. We present two real variants of the spectral decomposition and the real functional calculus theorems for unbounded normal operators acting in a real Hilbert space.