For a fixed n > 2, we study the set Λ of generalized idempotents, which are operators satisfying T n+1 = T. Also the subsets Λ†, of operators such that T n−1 is the Moore-Penrose pseudo-inverse of T, and Λ*, of operators such that T n−1 = T* (known as generalized projections) are studied. The local smooth structure of these sets is examined.
@article{bwmeta1.element.doi-10_2478_s11533-013-0230-z,
author = {Esteban Andruchow and Gustavo Corach and Mostafa Mbekhta},
title = {A note on the differentiable structure of generalized idempotents},
journal = {Open Mathematics},
volume = {11},
year = {2013},
pages = {1004-1019},
zbl = {1278.47003},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-013-0230-z}
}
Esteban Andruchow; Gustavo Corach; Mostafa Mbekhta. A note on the differentiable structure of generalized idempotents. Open Mathematics, Tome 11 (2013) pp. 1004-1019. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-013-0230-z/
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