| dc.contributor.author | Okello, Boaz Okoth | |
| dc.date.accessioned | 2023-02-14T12:35:07Z | |
| dc.date.available | 2023-02-14T12:35:07Z | |
| dc.date.issued | 2017 | |
| dc.identifier.uri | http://ir.jooust.ac.ke:8080/xmlui/handle/123456789/11836 | |
| dc.description.abstract | Elementary operators originated from the study of the Sylvester and Rosenblum equation AX - X B = Z. Although a lot of work on vari¬ous properties of elementary operators has been done, the norm property still remains an interesting area to many mathematicians with their up¬per norms in terms of their coefficients being trivially obtainable while obtaining them from below has proved to be a challenge. Studies on the norms of the elementary operators on J B* -algebras Prime C* -algebras, Calkin algebras and standard operator algebras have been considered. In this study we: Determine the norms of Jordan elementary operators; investigate the maximal numerical range and; establish the relationship between norms and maximal numerical radius of Jordan elementary op¬erators. To achieve this we use known fundamental mathematical results which are restated; The theory of numerical ranges together with techni¬cal approaches like tensor products and polar decompositions were also used. In this study we showed that the norm of Jordan elementary oper¬ator is 2, we also proved that the maximal numerical range is nonempty, closed and convex and lastly we showed that maximal numerical radius is equivalent to Jordan elementary operator norm but are not necessar¬ily equal. This study may be applicable in genetics in developments of mathematical models to understand how DNA is packed and unpacked in cells; Numerical ranges may be relevant to stability equations of one-step method for the numerical solution of boundary value problems in ODE and PDE; The study of norms can be useful in obtaining the least upper bound on the magnitude of the largest eigenvalue. | en_US |
| dc.language.iso | en | en_US |
| dc.publisher | JOOUST | en_US |
| dc.subject | Norms and Maximal Numerical Range | en_US |
| dc.subject | Jordan Elementary Operators | en_US |
| dc.title | Norms and Maximal Numerical Range of Jordan Elementary Operators | en_US |
| dc.type | Thesis | en_US |