Commuting Outer Inverses ()
Muneo Chō,
Gabriel Kantún-Montiel
Department of Mathematics, Faculty of Science, Kanagawa University, Kanagawa, Japan.
Department of Research and Graduate Studies, Linda Vista University, Pueblo Nuevo Solistahuacán, Mexico.
DOI: 10.4236/alamt.2013.34013
PDF HTML XML
2,769
Downloads
6,097
Views
Citations
Abstract
The group, Drazin and Koliha-Drazin inverses are particular classes of commuting outer inverses. In this note, we use the inverse along an element to study some spectral conditions related to these inverses in the case of bounded linear operators on a Banach space.
Share and Cite:
M. Chō and G. Kantún-Montiel, "Commuting Outer Inverses,"
Advances in Linear Algebra & Matrix Theory, Vol. 3 No. 4, 2013, pp. 69-72. doi:
10.4236/alamt.2013.34013.
Conflicts of Interest
The authors declare no conflicts of interest.
References
|
[1]
|
X. Mary, “On Generalized Inverses and Green’s Relations,” Linear Algebra Applications, Vol. 434, No. 8, 2011, pp. 1836-1844.
http://dx.doi.org/10.1016/j.laa.2010.11.045
|
|
[2]
|
G. Kantún-Montiel and S. V. Djordjevi?, “Invertibility along an Operator,” unpublished.
|
|
[3]
|
A. Dajic and J. J. Koliha, “The Sigma-g-Drazin Inverse and the Generalized Mbekhta Decomposition,” Integral Equations and Operator Theory, Vol. 57, No. 3, 2007, pp. 309-326. http://dx.doi.org/10.1007/s00020-006-1454-0
|
|
[4]
|
P. Aiena, “Fredholm and Local Spectral Theory, with Applications to Multipliers,” Kluwer Academic Publishers, Dordrecht-Boston-London, 2004.
|
|
[5]
|
J. J. Koliha, “A Generalized Drazin Inverse,” Glasgow Mathematical Journal, Vol. 38, No. 3, 1996, pp. 367-381.
http://dx.doi.org/10.1017/S0017089500031803
|