Pairs of Projections on a Hilbert Space

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Pairs of Projections on a Hilbert Space
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Total Pages : 42
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ISBN-10 : 9175199327
ISBN-13 : 9789175199320
Rating : 4/5 (27 Downloads)

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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.


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