A note on the differentiable structure of generalized idempotents

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.