Maps Preserving Complementarity of Closed Subspaces of a Hilbert Space

Let and be infinite-dimensional separable Hilbert spaces and Lat the lattice of all closed subspaces oh . We describe the general form of pairs of bijective maps ϕ, Ψ : Lat → Lat having the property that for every pair U, V ∊ Lat we have . Then we reformulate this theorem as a description of bijective image equality and kernel equality preserving maps acting on bounded linear idempotent operators. Several known structural results for maps on idempotents are easy consequences.

The Group Inverse of the Combinations of Two Idempotent Operators

We present some inverses and group inverses results for linear combinations of two idempotents and their products.

On the Idempotent Solutions of a Kind of Operator Equations

This paper provides some relations between the idempotent operators and the solutions to operator equations ABA=A2 and BAB=B2.