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A note on the differentiable structure of generalized idempotents |
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| Authors: | Esteban Andruchow Gustavo Corach Mostafa Mbekhta |
| Institution: | 1230. Instituto de Ciencias, Universidad Nacional de Gral. Sarmiento, J.M. Gutierrez 1150, 1613, Los Polvorines, Argentina 2230. Instituto Argentino de Matemática, Saavedra 15, 3er. piso, 1083, Buenos Aires, Argentina 3230. Facultad de Ingeniería, Universidad de Buenos Aires, 1073, Buenos Aires, Argentina 4230. UFR de Mathématiques, CNRS-UMR 8524, Université Lille 1, 59665, Villeneuve d’Ascq, France |
| Abstract: | 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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