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On the invertibility of linear sums of two idempotents and of two square zero operators

Let P and Q be two idempotents, we review the results about the equivalence between the
invertibility of a linear combination aP +bQ and that of P +Q, where a and b are any nonzero
complex numbers with a + b
eq 0. It is possible to extend the results to the case P and Q are
square-zero elements. However, we will show that these extensions are impossible in general
for P and Q being partial isometries or n-potents with n geq 3. We will show in case P and Q
are square-zero elements, the invertibility of P +Q is equivalent to that of aP +bQ for nonzero
a, b.

Identiferoai:union.ndltd.org:NSYSU/oai:NSYSU:etd-0709107-162359
Date09 July 2007
CreatorsWang, Chih-jen
ContributorsJyh-Shyang Jeang, Hwa-Long Gau, Mu-Ming Wong, Mark C. Ho, Ngai-Ching Wong
PublisherNSYSU
Source SetsNSYSU Electronic Thesis and Dissertation Archive
LanguageEnglish
Detected LanguageEnglish
Typetext
Formatapplication/pdf
Sourcehttp://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0709107-162359
Rightswithheld, Copyright information available at source archive

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