Mutie KavilaMaina, George Kariuki2021-10-292021-10-292021http://ir-library.ku.ac.ke/handle/123456789/22889A Research Project Submitted in Partial Fulfillment of the Requirements for the Award of the Degree of Masters of Science (Pure Mathematics) in the School of Pure and Applied Sciences, Kenyatta University July 2021There are several well-developed theorems, lemmas and propositions relating to normaloid, convexoid, spectraloid and transloid operators. It has been demonstrated that every nor- maloid operator is spectraloid and that every convexoid operator is spectraloid. In ad- dition, several researchers have extended interesting and signi cant properties of these operators. However, they do not constitute deeper and useful generalizations and there still does not exist a comprehensive investigation of the properties under which these op- erators relate to one another. In this project, we have established the essential properties and characterizations of these operators. Moreover, we have given generalized results in a Hilbert space using relevant theorems, propositions and corollaries. Lastly, we have inves- tigated conditions under which normaloid and convexiod operators relate to one another.enPropertiesCharacterizationsNormaloidConvexoidTransloidSpectraloid OperatorsHilbert SpacesThesis