On joint essential maximal numerical ranges

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dc.contributor.authorOmoke, Priscah Mogotu
dc.date.accessioned2021-05-12T09:57:58Z
dc.date.available2021-05-12T09:57:58Z
dc.date.issued2017
dc.descriptionPaper presented at the 4th Strathmore International Mathematics Conference (SIMC 2017), 19 - 23 June 2017, Strathmore University, Nairobi, Kenya.en_US
dc.description.abstractThe study of numerical range of an operator has been an area of intense research. The motivation for the development arose from the classical theory of quadratic forms. It forms a very important aspect in functional analysis, operator theory and its applications to economics, quantum chemistry and quantum computing amongst other fields. A lot of results have been obtained on numerical ranges particularly by Fong, Khan among others. The concept of maximal numerical ranges of a bounded operator T E B (H) was studied by Stampfli who used it to derive an identity for the norm of derivation. This concept was later generalized by Ghan to the joint maximal numerical ranges of m- tuples of operator. The joint essential maximal numerical range was studied by Khan and established that the joint essential maximal numerical range can be empty. In this paper we have showed that the joint essential maximal numerical range is nonempty, compact and convex. We also established that each element in the joint essential maximal numerical range is a star centre of the joint maximal numerical range. The result obtained show that star-shapedness is related to convexity in that a convex set is starshaped with all its points being star centres.en_US
dc.description.sponsorshipJaramogi Oginga Odinga University of Science and Technology, Box 210-40601, Bondo-Kenya.en_US
dc.identifier.urihttp://hdl.handle.net/11071/11837
dc.language.isoenen_US
dc.publisherStrathmore Universityen_US
dc.subjectNumerical rangeen_US
dc.subjectJoint maximal numerical rangeen_US
dc.subjectJoint essential maximal numerical rangeen_US
dc.subjectConvexityen_US
dc.subjectConvergenceen_US
dc.titleOn joint essential maximal numerical rangesen_US
dc.typeArticleen_US
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