Mixed-Type Reverse Order Laws for Generalized Inverses over Hilbert Space - Applied Mathematics

AM > Vol.8 No.5, May 2017

Applied Mathematics

Volume 8, Issue 5 (May 2017)

ISSN Print: 2152-7385 ISSN Online: 2152-7393

Google-based Impact Factor: 0.58 Citations

Mixed-Type Reverse Order Laws for Generalized Inverses over Hilbert Space ()

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DOI: 10.4236/am.2017.85050 6,367 Downloads 6,996 Views Citations

Author(s)

Haiyan Zhang, Fengling Lu

Affiliation(s)

College of Mathematics and Satistics, Shangqiu Normal University, Shangqiu, China.

ABSTRACT

In this paper, by using a block-operator matrix technique, we study mixed-type reverse order laws for {1,3}-, {1,2,3}- and {1,3,4}-generalized inverses over Hilbert spaces. It is shown that

and

when the ranges of are closed. Moreover, a new equivalent condition of

is given.

KEYWORDS

{1, 2, 3}-Reverse, {1, 3, 4}-Reverse, Reverse Order Law, Block-Operator Matrix

Share and Cite:

Zhang, H. and Lu, F. (2017) Mixed-Type Reverse Order Laws for Generalized Inverses over Hilbert Space. Applied Mathematics, 8, 637-644. doi: 10.4236/am.2017.85050.

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