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Pairs of projections on a Hilbert space:properties and generalized invertibility
Linköping University, Department of Mathematics. Linköping University, The Institute of Technology.
2012 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

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.

Place, publisher, year, edition, pages
Linköping University Electronic Press, 2012. , 42 p.
Series
Linköping Studies in Science and Technology. Thesis, ISSN 0280-7971 ; 1525
National Category
Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-75909ISBN: 978-91-7519-932-0 (print)OAI: oai:DiVA.org:liu-75909DiVA: diva2:510422
Presentation
2012-04-16, Alan Turing, Building E, Campus Valla, Linköpings universitet, Linköping, 10:15 (English)
Opponent
Supervisors
Available from: 2012-03-28 Created: 2012-03-16 Last updated: 2012-05-14Bibliographically approved
List of papers
1. On pairs of generalized and hypergeneralized projections on a Hilbert space
Open this publication in new window or tab >>On pairs of generalized and hypergeneralized projections on a Hilbert space
2012 (English)Report (Other academic)
Abstract [en]

In this paper, we characterize generalized and hypergeneralized projections (bounded linear operators which satisfy conditions A2=A*and A2=A). We give theirs matrix representations and examine under what conditions the products, differences, and sums of these operators are operators of the same class.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2012. 16 p.
Series
LiTH-MAT-R, ISSN 0348-2960 ; 2012:01
Keyword
generalized projections, hypergeneralized projections
National Category
Mathematics
Identifiers
urn:nbn:se:liu:diva-74783 (URN)LiTH-MAT-R–2012/01–SE (ISRN)
Available from: 2012-03-13 Created: 2012-02-08 Last updated: 2012-03-28Bibliographically approved
2. On the Moore-Penrose and the Drazin inverse of two projections on Hilbert space
Open this publication in new window or tab >>On the Moore-Penrose and the Drazin inverse of two projections on Hilbert space
2012 (English)Report (Other academic)
Abstract [en]

For two given orthogonal, generalized or hypergeneralized projectionsP and Q on Hilbert space H, we gave their matrix representation. We also gave canonical forms of the Moore-Penrose and the Drazin inverses of their product, difference and sum. In addition, it is showed when these operators are EP and some simple correlations between mentioned operators are established.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2012. 16 p.
Series
LiTH-MAT-R, ISSN 0348-2960 ; 2012:03
Keyword
Moore-penrose inverse, Drazin inverse, generalized projection, hypergeneralized projection
National Category
Mathematics
Identifiers
urn:nbn:se:liu:diva-75869 (URN)LiTH-MAT-R–2012/03–SE (ISRN)
Available from: 2012-03-13 Created: 2012-03-13 Last updated: 2012-03-28Bibliographically approved

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Radosavljevic, Sonja

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