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Die ongelykheid van Johann von Neumann
Tesis (M. Sc.) -- Universiteit van Stellenbosch, 1996.
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| Format: | Thesis |
| Language: | Afrikaans |
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Stellenbosch : Stellenbosch University
2012
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| _version_ | 1867613902087389184 |
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| access_status_str | Open Access |
| author | Du Preez, Francois Albertus |
| author2 | Muller, M. A. |
| author_browse | Du Preez, Francois Albertus Muller, M. A. |
| author_facet | Muller, M. A. Du Preez, Francois Albertus |
| author_sort | Du Preez, Francois Albertus |
| collection | Thesis |
| dc_rights_str_mv | Stellenbosch University |
| description | Tesis (M. Sc.) -- Universiteit van Stellenbosch, 1996. |
| format | Thesis |
| id | oai:scholar.sun.ac.za:10019.1/55076 |
| institution | Stellenbosch University (South Africa) |
| language | Afrikaans |
| last_indexed | 2026-06-10T12:43:30.888Z |
| license_str | Other — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from SUNScholar — Stellenbosch University Repository |
| publishDate | 2012 |
| publishDateRange | 2012 |
| publishDateSort | 2012 |
| publisher | Stellenbosch : Stellenbosch University |
| publisherStr | Stellenbosch : Stellenbosch University |
| record_format | dspace |
| source_str | SUNScholar — Stellenbosch University Repository |
| spelling | oai:scholar.sun.ac.za:10019.1/55076 Die ongelykheid van Johann von Neumann Du Preez, Francois Albertus Muller, M. A. Stellenbosch University. Faculty of Science. Dept. of Mathematical Sciences. Von Neumann, John, -- 1903-1957 Linear operators Hilbert space Von Neumann algebras Dissertations -- Mathematics Tesis (M. Sc.) -- Universiteit van Stellenbosch, 1996. In this thesis we discuss linear operators on a Hilbert space, where the space is complex or real. The purpose is to prove the inequality of Johann von Neumann (1903-1957), illustrate the inequality for special cases, and to prove how a Hilbert space can be characterized by means of this inequality. The necessary definitions and theorems are given in the first three chapters. In chapter 1 the emphasis is on the properties of linear operators on Hilbert space, isometries, unitary operators, self-adjoint operators and projections. In chapter 2 we show how shift operators are used to write Hilbert spaces in terms of orthogonal sums. In chapter 3, contractions are discussed, since the inequality of Von Neumann is valid for contractions. In chapter 4 we discuss the concept and construction of a dilation, since it is important for the proof of the inequality of Von Neumann, which is proved at the end of the chapter. The work in these chapters, is mainly taken from. In chapter 5 it is shown how a Hilbert space can be characterized by the inequality of Von Neumann, according to the proof by Foias. In chapter 6 we discuss the extensions of this inequality, as well as examples where the inequality is not valid ([1],[4],[6],[7],[8],[9]). I would like to express my gratitude towards my promotor, Dr. M.A. Muller, for his assistance, and patience, as well as his quest for precision. I also wish to express my sincere appreciation towards Miss H.C. Oberholzer for the neat typing and patience. Masters 2012-08-27T11:36:52Z 2012-08-27T11:36:52Z 1996 Thesis http://hdl.handle.net/10019.1/55076 af Stellenbosch University 100 pages application/pdf Stellenbosch : Stellenbosch University |
| spellingShingle | Von Neumann, John, -- 1903-1957 Linear operators Hilbert space Von Neumann algebras Dissertations -- Mathematics Du Preez, Francois Albertus Die ongelykheid van Johann von Neumann |
| title | Die ongelykheid van Johann von Neumann |
| title_full | Die ongelykheid van Johann von Neumann |
| title_fullStr | Die ongelykheid van Johann von Neumann |
| title_full_unstemmed | Die ongelykheid van Johann von Neumann |
| title_short | Die ongelykheid van Johann von Neumann |
| title_sort | die ongelykheid van johann von neumann |
| topic | Von Neumann, John, -- 1903-1957 Linear operators Hilbert space Von Neumann algebras Dissertations -- Mathematics |
| url | http://hdl.handle.net/10019.1/55076 |
| work_keys_str_mv | AT dupreezfrancoisalbertus dieongelykheidvanjohannvonneumann |