Equalities of ideals associated with two projections in rings with involution
Julio Benítez, Dragana S. Cvetković‐Ilić · Linear and Multilinear Algebra · 2012
In this article we study various right ideals associated with two projections (self-adjoint idempotents) in a ring with involution. Results of O.M. Baksalary, G. Trenkler, R. Piziak, P.L. Odell and R. Hahn about orthogonal projectors (complex matrices which are Hermitian and idempotent) are considered in the setting of rings with involution. New proofs based on algebraic arguments, rather than finite-dimensional and rank theory, are given.