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Isometries on symmetric spaces associated with semi-finite von Neumann algebras
Isometries on Banach spaces of measurable functions can typically be characterized as weighted composition operators. In the non-commutative setting, isometries between symmetric spaces (of trace-measurable operators) can often be described in terms of a Jordan ✽-homomorphism (which may be consid...
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| Format: | Thesis |
| Language: | English |
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Department of Mathematics and Applied Mathematics
2017
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| _version_ | 1867613244658548736 |
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| access_status_str | Open Access |
| author | De Jager, Pierre |
| author2 | Conradie, Jurie J |
| author_browse | Conradie, Jurie J De Jager, Pierre |
| author_facet | Conradie, Jurie J De Jager, Pierre |
| author_sort | De Jager, Pierre |
| collection | Thesis |
| description | Isometries on Banach spaces of measurable functions can typically be characterized as weighted composition operators. In the non-commutative setting, isometries between symmetric spaces (of trace-measurable operators) can often be described in terms of a Jordan ✽-homomorphism (which may be considered a non-commutative composition operator) weighted by a partial isometry and/or a positive operator. In this thesis we describe the structures of isometries on various (non-commutative) symmetric spaces associated with semi-finite von Neumann algebras. This is achieved by extending certain results from the finite setting to the semi-finite setting, exploring the applicability of disjointness-preserving techniques in generalizations of Lₚ-spaces, and developing characterizations of extreme points in a certain class of Lorentz spaces and in various types of Orlicz spaces. |
| format | Thesis |
| id | oai:open.uct.ac.za:11427/25167 |
| institution | University of Cape Town (South Africa) |
| language | eng |
| last_indexed | 2026-06-10T12:33:04.194Z |
| license_str | Not specified — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UCTD — University of Cape Town Open Access Repository |
| publishDate | 2017 |
| publishDateRange | 2017 |
| publishDateSort | 2017 |
| publisher | Department of Mathematics and Applied Mathematics |
| publisherStr | Department of Mathematics and Applied Mathematics |
| record_format | dspace |
| source_str | UCTD — University of Cape Town Open Access Repository |
| spelling | oai:open.uct.ac.za:11427/25167 Isometries on symmetric spaces associated with semi-finite von Neumann algebras De Jager, Pierre Conradie, Jurie J Martin, R T W Mathematics Isometries on Banach spaces of measurable functions can typically be characterized as weighted composition operators. In the non-commutative setting, isometries between symmetric spaces (of trace-measurable operators) can often be described in terms of a Jordan ✽-homomorphism (which may be considered a non-commutative composition operator) weighted by a partial isometry and/or a positive operator. In this thesis we describe the structures of isometries on various (non-commutative) symmetric spaces associated with semi-finite von Neumann algebras. This is achieved by extending certain results from the finite setting to the semi-finite setting, exploring the applicability of disjointness-preserving techniques in generalizations of Lₚ-spaces, and developing characterizations of extreme points in a certain class of Lorentz spaces and in various types of Orlicz spaces. 2017-09-14T12:14:24Z 2017-09-14T12:14:24Z 2017 Doctoral Thesis Doctoral PhD http://hdl.handle.net/11427/25167 eng application/pdf Department of Mathematics and Applied Mathematics Faculty of Science University of Cape Town |
| spellingShingle | Mathematics De Jager, Pierre Isometries on symmetric spaces associated with semi-finite von Neumann algebras |
| thesis_degree_str | Doctoral |
| title | Isometries on symmetric spaces associated with semi-finite von Neumann algebras |
| title_full | Isometries on symmetric spaces associated with semi-finite von Neumann algebras |
| title_fullStr | Isometries on symmetric spaces associated with semi-finite von Neumann algebras |
| title_full_unstemmed | Isometries on symmetric spaces associated with semi-finite von Neumann algebras |
| title_short | Isometries on symmetric spaces associated with semi-finite von Neumann algebras |
| title_sort | isometries on symmetric spaces associated with semi finite von neumann algebras |
| topic | Mathematics |
| url | http://hdl.handle.net/11427/25167 |
| work_keys_str_mv | AT dejagerpierre isometriesonsymmetricspacesassociatedwithsemifinitevonneumannalgebras |