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.
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G. Kantún-Montiel and S. V. Djordjevi?, “Invertibility along an Operator,” unpublished.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
