CEU Electronic Theses and Dissertations, 2023
| Author | Ramanantoanina, Andriamanankasina |
|---|---|
| Title | Partial Orders on Positive Hilbert Space Operators and Related Preserver Problems |
| Summary | This thesis contributes to the study of two important partial orders on the set of positive Hilbert space operators: the Löwner order or usual order, and the Olson order which is commonly called the spectral order. We explore some faithful representations of positive operators on structures of real valued functions defined on the unit sphere of the underlying Hilbert space. These representations turn the usual order and the spectral order to pointwise order among the representing functions. The investigation of the algebraic structures of the representing functions reveals a surprising compatibility with the arithmetic and harmonic means, which are examples of Kubo-Ando means, a family of binary operations closely related to the usual order. This lead us to study the analogue of Kubo-Ando operator means with respect to the spectral order. |
| Supervisor | Molnár, Lajos |
| Department | Mathematics PhD |
| Full text | https://www.etd.ceu.edu/2023/ramanantoanina_an02.pdf |
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