Opuscula Math. 38, no. 5 (2018), 597-621
https://doi.org/10.7494/OpMath.2018.38.5.597

Opuscula Mathematica

# The spectral theorem for locally normal operators

Aurelian Gheondea

Abstract. We prove the spectral theorem for locally normal operators in terms of a locally spectral measure. In order to do this, we first obtain some characterisations of local projections and we single out and investigate the concept of a locally spectral measure.

Keywords: locally Hilbert space, locally $$C^*$$-algebra, locally normal operator, local projection, locally spectral measure.

Mathematics Subject Classification: 47B15, 46A13, 46C05.

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• Aurelian Gheondea
• Bilkent University, Department of Mathematics, 06800 Bilkent, Ankara, Turkey
• Institutul de Matematică al Academiei Române, C.P., 1-764, 014700 Bucuresti, România
• Communicated by P.A. Cojuhari.
• Revised: 2018-05-14.
• Accepted: 2018-05-15.
• Published online: 2018-06-12.