Opuscula Math. 38, no. 5 (2018), 597-621
The spectral theorem for locally normal operators
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.