×

Outer generalized inverses in rings. (English) Zbl 1111.15007

Summary: We formulate basic results on outer generalized inverses of elements in rings. We characterize elements which have the same idempotents related to their particular outer generalized inverses and investigate positive generalized inverses in \(C^*\)-algebras.

MSC:

15A09 Theory of matrix inversion and generalized inverses
16S10 Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.)
46L05 General theory of \(C^*\)-algebras
47A05 General (adjoints, conjugates, products, inverses, domains, ranges, etc.)
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Ben-Israel A., Generalized Inverses: Theory and Applications., 2. ed. (2003)
[2] Bouldin R. H., Pitman Ser. Res. Notes in Math. 66 pp 233– (1982)
[3] Caradus S. R., Generalized Inverses and Operator Theory (1978) · Zbl 0434.47003
[4] DOI: 10.1016/S0024-3795(00)00101-4 · Zbl 0963.15002 · doi:10.1016/S0024-3795(00)00101-4
[5] DOI: 10.1080/0003681021000004474a · Zbl 1044.47010 · doi:10.1080/0003681021000004474a
[6] Djordjević D. S., Publ. Math. Debrecen 59 (1) pp 147– (2001)
[7] DOI: 10.2307/2308576 · Zbl 0083.02901 · doi:10.2307/2308576
[8] Harte R. E., Panam. Math. J. 1 pp 10– (1991)
[9] Harte R. E., Studia Math. 103 pp 71– (1992)
[10] DOI: 10.1017/S0017089500031803 · Zbl 0897.47002 · doi:10.1017/S0017089500031803
[11] Koliha J. J., Math. Proc. Royal Irish Acad. 99 pp 17– (1999)
[12] DOI: 10.1017/S1446788700003657 · Zbl 0999.16025 · doi:10.1017/S1446788700003657
[13] DOI: 10.1080/01630568708816235 · Zbl 0633.47001 · doi:10.1080/01630568708816235
[14] DOI: 10.1016/B978-0-12-514250-2.50005-6 · doi:10.1016/B978-0-12-514250-2.50005-6
[15] DOI: 10.1137/0148095 · Zbl 0661.15002 · doi:10.1137/0148095
[16] DOI: 10.1017/S0305004100030401 · doi:10.1017/S0305004100030401
[17] Stanimirović P. S., Acta Math. Hungar. 92 (1) pp 121– (2001)
[18] DOI: 10.1016/S0377-0427(00)00710-X · Zbl 0993.15003 · doi:10.1016/S0377-0427(00)00710-X
[19] DOI: 10.1080/00207160108805075 · Zbl 0986.65038 · doi:10.1080/00207160108805075
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.