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THE DRAZIN INVERSES OF PRODUCTS AND DIFFERENCES OF PROJECTIONS IN A C*-ALGEBRA

Part of: Basic linear algebra Numerical linear algebra

Published online by Cambridge University Press:  01 April 2009

YUAN LI
YUAN LI*
Affiliation:
College of Mathematics and Information Science, Shaanxi Normal University, Xi’an 710062, People’s Republic of China (email: liyuan0401@yahoo.com.cn)
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Abstract

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For two given projections p and q in a C*-algebra, we investigate how to express the Drazin inverses of the product pq and the difference p−q, and give applications. As a special case, we obtain the results of [C. Y. Deng, ‘The Drazin inverses of products and differences of orthogonal projections’, J. Math. Anal. Appl.335 (2007) 64–71], with considerably simpler proofs.

Keywords

Drazin inverseprojection

MSC classification

Secondary: 15A09: Matrix inversion, generalized inverses 65F20: Overdetermined systems, pseudoinverses
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 86 , Issue 2 , April 2009 , pp. 189 - 198
Copyright
Copyright © Australian Mathematical Society 2009

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