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A note on the differentiable structure of generalized idempotents

Esteban Andruchow, Gustavo Corach, Mostafa Mbekhta (2013)

Open Mathematics

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.

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