This thesis is concerned with the problem of characterizing sums, differences, and products of two projections on a separable Hilbert space. Other objective is characterizing the Moore-Penrose and the Drazin inverse for pairs of operators. We use reasoning similar to one presented in the famous P. Halmos’ two projection theorem: using matrix representation of two orthogonal projection depending on the relations between their ranges and null-spaces gives us simpler form of their matrices and allows us to involve matrix theory in solving problems. We extend research to idempotents, generalized and hypergeneralized projections and their combinations.
| Identifer | oai:union.ndltd.org:UPSALLA1/oai:DiVA.org:liu-75909 |
| Date | January 2012 |
| Creators | Radosavljevic, Sonja |
| Publisher | Linköpings universitet, Matematiska institutionen, Linköpings universitet, Tekniska högskolan |
| Source Sets | DiVA Archive at Upsalla University |
| Language | English |
| Detected Language | English |
| Type | Licentiate thesis, comprehensive summary, info:eu-repo/semantics/masterThesis, text |
| Format | application/pdf |
| Rights | info:eu-repo/semantics/openAccess |
| Relation | Linköping Studies in Science and Technology. Thesis, 0280-7971 ; 1525 |
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