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Linear and Multilinear Algebra Volume 59, 2011 - Issue 3
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Original Articles

Additive results for the group inverse in an algebra with applications to block operators

Julio Benítez Departamento de Matemática Aplicada, Instituto de Matemática Multidisciplinar, Universidad Politécnica de Valencia, Camino de Vera s/n, 46022, Valencia, SpainCorrespondence[email protected]
,
Xiaoji Liu College of Mathematics and Computer Science, Guangxi University for Nationalities, Nanning 530006, P.R. China
&
Tongping Zhu College of Mathematics and Computer Science, Guangxi University for Nationalities, Nanning 530006, P.R. China
Pages 279-289 | Received 13 May 2009, Accepted 12 Oct 2009, Published online: 25 Feb 2011
 
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Abstract

We derive a very short expression for the group inverse of a 1 + ··· + a n when a 1, … , a n are elements in an algebra having group inverse and satisfying a i a j  = 0 for i < j. We apply this formula in order to find the group inverse of 2 × 2 block operators under some conditions.

AMS Subject Classifications:

Acknowledgements

X. Liu and T. Zhu are supported by Guangxi Science Foundation (0640016, 0832084).

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