A cone K in a vector space X is a subset which is closed under addition, positive scalar multiplication and the only element with additive inverse is zero. The pair (X, K) is called an ordered vector space. In this study, we consider the characterizations of reflexive Banach spaces. This is done by considering cones with bounded and unbounded bases and the second characterization is by reflexive cones. The relationship between cones with bounded and unbounded bases and reflexive cones is also considered. We provide an example to show distinction between such cones. / Dissertation (MSc (Mathematics))--University of Pretoria 2020. / UCDP - 523 / Mathematics and Applied Mathematics / MSc (Mathematics) / Unrestricted
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:up/oai:repository.up.ac.za:2263/78565 |
| Date | 12 1900 |
| Creators | Mbambo, S.P. |
| Contributors | Mabula, Mokhwetha D., u19377712@tuks.co.za |
| Publisher | University of Pretoria |
| Source Sets | South African National ETD Portal |
| Language | English |
| Detected Language | English |
| Type | Dissertation |
| Rights | © 2019 University of Pretoria. All rights reserved. The copyright in this work vests in the University of Pretoria. No part of this work may be reproduced or transmitted in any form or by any means, without the prior written permission of the University of Pretoria. |
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