NON-LINEAR MAPS BETWEEN SUBSETS OF BANACH SPACES
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Kent State University / OhioLINK
2009
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| Online Access: | http://rave.ohiolink.edu/etdc/view?acc_num=kent1251217291 |
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ndltd-OhioLink-oai-etd.ohiolink.edu-kent12512172912021-08-03T05:37:07Z NON-LINEAR MAPS BETWEEN SUBSETS OF BANACH SPACES Sbeih, Reema Mathematics d2 SCALING DOWN MAPS ln d1 b2 scaling down projection There is an extensive literature on linear maps and operators on Banach spaces. However, a corresponding non-linear theory is still in its beginning. We study non-linear maps between subsets of the classical Banach spaces and give estimates for the Banach-Mazur Lipschitz norm for some of the natural non-linear maps between unit spheres of these spaces. We show that the Banach-Mazur norm of these maps is much larger than the corresponding linear norms. We also study projections onto unit spheres of Banach spaces, we show that the scaling down projection is the best projection in <i>L</i><sup>1</sup>(0,1), and we give estimates for the <i>L</i><sup><i>p</i></sup>-spaces, <i>p</i>>1. 2009-09-24 English text Kent State University / OhioLINK http://rave.ohiolink.edu/etdc/view?acc_num=kent1251217291 http://rave.ohiolink.edu/etdc/view?acc_num=kent1251217291 unrestricted This thesis or dissertation is protected by copyright: all rights reserved. It may not be copied or redistributed beyond the terms of applicable copyright laws. |
| collection |
NDLTD |
| language |
English |
| sources |
NDLTD |
| topic |
Mathematics d2 SCALING DOWN MAPS ln d1 b2 scaling down projection |
| spellingShingle |
Mathematics d2 SCALING DOWN MAPS ln d1 b2 scaling down projection Sbeih, Reema NON-LINEAR MAPS BETWEEN SUBSETS OF BANACH SPACES |
| author |
Sbeih, Reema |
| author_facet |
Sbeih, Reema |
| author_sort |
Sbeih, Reema |
| title |
NON-LINEAR MAPS BETWEEN SUBSETS OF BANACH SPACES |
| title_short |
NON-LINEAR MAPS BETWEEN SUBSETS OF BANACH SPACES |
| title_full |
NON-LINEAR MAPS BETWEEN SUBSETS OF BANACH SPACES |
| title_fullStr |
NON-LINEAR MAPS BETWEEN SUBSETS OF BANACH SPACES |
| title_full_unstemmed |
NON-LINEAR MAPS BETWEEN SUBSETS OF BANACH SPACES |
| title_sort |
non-linear maps between subsets of banach spaces |
| publisher |
Kent State University / OhioLINK |
| publishDate |
2009 |
| url |
http://rave.ohiolink.edu/etdc/view?acc_num=kent1251217291 |
| work_keys_str_mv |
AT sbeihreema nonlinearmapsbetweensubsetsofbanachspaces |
| _version_ |
1719422553284411392 |