2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/152314We show the possibility and the uniqueness of polar decomposition of elements of arbitrary AW*-algebras inside them. We prove that spectral decomposition of normal elements of normal AW*-algebras is possible and unique inside them. The possibility of spectral decomposition of normal elements does not depend on the normality of the AW*-algebra under consideration.7 pages, LATEX, preprint NTZ-25/91 (Universitaet Leipzig, Naturwissenschaftlich-Theoretisches Zentrum, 1991), submitted to Zeitschr. Anal. AnwFunctional AnalysisOperator Algebrastext