On X-normed spaces and operator theory on c_0 over a field with a Krull valuation of arbitrary rank
| dc.contributor.author | Barría Comicheo, Angel | |
| dc.contributor.examiningcommittee | Zorboska, Nina (Mathematics) | en_US |
| dc.contributor.examiningcommittee | Sirker, Jesko (Physics and Astronomy) | en_US |
| dc.contributor.examiningcommittee | Diagana, Toka (University of Alabama) | en_US |
| dc.contributor.supervisor | Shamseddine, Khodr (Mathematics) Craigen, Rob (Mathematics) | en_US |
| dc.date.accessioned | 2018-11-30T16:58:12Z | |
| dc.date.available | 2018-11-30T16:58:12Z | |
| dc.date.issued | 2018-11-28 | en_US |
| dc.date.submitted | 2018-11-30T16:31:44Z | en |
| dc.degree.discipline | Mathematics | en_US |
| dc.degree.level | Doctor of Philosophy (Ph.D.) | en_US |
| dc.description.abstract | Between 2013 and 2015 Aguayo et al. developed an operator theory on the space c0 of null sequences in the complex Levi-Civita field by defining an inner product on c0 that induces the supremum norm on c0 and then studying compact and self-adjoint operators on c0, thus presenting a striking analogy between c0 over the complex Levi-Civita field and the Hilbert space l2 over the complex numbers field. In this thesis, the author tries to obtain these results in the most general case possible by considering a base field with a Krull valuation taking values in an arbitrary commutative group. This leads to the concept of X-normed spaces, which are spaces with norms taking values in a totally ordered set X not necessarily embedded in the field of real numbers. | en_US |
| dc.description.note | February 2019 | en_US |
| dc.identifier.citation | Barria Comicheo, A., and Shamseddine, K. Summary on non-Archimedean valued fields. In Advances in Ultrametric Analysis (2018), A. Escassut, C. Perez-Garcia, and K. Shamseddine, Eds., vol. 704 of Contemporary Mathematics, Providence, RI: American Mathematical Society, pp. 1–36. | en_US |
| dc.identifier.uri | http://hdl.handle.net/1993/33572 | |
| dc.language.iso | eng | en_US |
| dc.rights | open access | en_US |
| dc.subject | non-Archimedean Functional Analysis | en_US |
| dc.subject | Operator theory | en_US |
| dc.subject | Non-Archimedean valued fields | en_US |
| dc.title | On X-normed spaces and operator theory on c_0 over a field with a Krull valuation of arbitrary rank | en_US |
| dc.type | doctoral thesis | en_US |