Properties and Characterizations of Normaloid, Convexoid, Transloid and Spectraloid Operators in Hilbert Spaces

Abstract

There 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.