A note on the differentiable structure of generalized idempotents

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Abstract

For a fixed n > 2, we study the set Λ of generalized idempotents, which are operators satisfying Tn+1 = T. Also the subsets Λ†, of operators such that Tn-1 is the Moore-Penrose pseudo-inverse of T, and Λ*, of operators such that Tn-1 = T* (known as generalized projections) are studied. The local smooth structure of these sets is examined. © 2013 Versita Warsaw and Springer-Verlag Wien.

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Andruchow, E., Corach, G., & Mbekhta, M. (2013). A note on the differentiable structure of generalized idempotents. Central European Journal of Mathematics, 11(6), 1004–1019. https://doi.org/10.2478/s11533-013-0230-z

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