On the operator equations An = A*A
Souheyb Dehimi, Mohammed Hichem Mortad, Zsigmond Tarcsay · Linear and Multilinear Algebra · 2019
Let n∈N and let A be a closed linear operator (everywhere bounded or unbounded). In this paper, we study (among others) equations of the type A∗A=An where n≥2 and see when they yield A=A∗ (or a weaker class of operators). In case n≥3, we have in fact a new class of operators which could placed right after orthogonal projections and just before normal operators.