The spectral theorem for locally normal operators

• Main Author: Aurelian Gheondea
• Format: Article
• Language: English
• Published: AGH Univeristy of Science and Technology Press 2018-01-01
• Series: Opuscula Mathematica
• Subjects: locally Hilbert space; locally \(C^*\)-algebra; locally normal operator; local projection; locally spectral measure
• Online Access: http://www.opuscula.agh.edu.pl/vol38/5/art/opuscula_math_3827.pdf
• ISSN: 1232-9274

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.