A note on the differentiable structure of generalized idempotents

Abstract

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