Pairs of Projections on a Hilbert Space
Author | : |
Publisher | : |
Total Pages | : 42 |
Release | : 2012 |
ISBN-10 | : 9175199327 |
ISBN-13 | : 9789175199320 |
Rating | : 4/5 (27 Downloads) |
Book excerpt: 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.