Ampeire, Anitah2024-10-222024-10-222024Ampeire, Anitah (2024). Operator Theory on Hilbert Spaces. Kabale: Kabale University.http://hdl.handle.net/20.500.12493/2339Functional analysis, particularly the study of Operator theory on Hilbert spaces, plays a pivotal role in mathematics and its applications across various disciplines. This research report aims to conduct a comprehensive study on the significance of Operator theory on Hilbert spaces in functional analysis. The proposal delves into the fundamental properties and characteristics of Hilbert spaces, the properties and classifications of operators, the implications of the Spectral Theorem for self-adjoint operators, and their applications in mathematics and related fields. Through a mixed-methods approach, including literature review and thematic analysis, the study seeks to provide a holistic understanding of these concepts and their practical implications.enAttribution-NonCommercial-NoDerivs 3.0 United Stateshttp://creativecommons.org/licenses/by-nc-nd/3.0/us/Operator TheoryHilbert SpacesArticle