Properties and Characterizations of Normaloid, Convexoid, Transloid and Spectraloid Operators in Hilbert Spaces
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Date
2021
Authors
Maina, George Kariuki
Journal Title
Journal ISSN
Volume Title
Publisher
Kenyatta University
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.
Description
A 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 2021
Keywords
Properties, Characterizations, Normaloid, Convexoid, Transloid, Spectraloid Operators, Hilbert Spaces