CEU Electronic Theses and Dissertations, 2020
| Author | Ramanantoanina, Andriamanankasina |
|---|---|
| Title | Positive Hilbert Space Operators as Real Valued Functions |
| Summary | This essay is a short exploration of functional representations of positive Hilbert space operators. These are non-negative functions associated to positive operators in a way that that transfers order structures of operators into pointwise order on the functions. The orders of interest here are the usual L\"owner order and the spectral order. The representations are built to behave well with the orders but they present interesting algebraic and topological properties like compatibility with mean operations and continuous functional calculus. We present here an application of this machinery to describe the spectral order isomorphism group of the set of selfadjoint operators on infinite dimensional Hilbert spaces. |
| Supervisor | Molnar, Lajos |
| Department | Mathematics Ps |
| Full text | https://www.etd.ceu.edu/2020/ramanantoanina_an02.pdf |
Visit the CEU Library.
© 2007-2021, Central European University