Path connectivity of k-generalized projectors Original Research Article

Let image be the set of all bounded linear operators on a Hilbert space H. An operator image is said to be a k-generalized projector if Ak=A*, where kgreater-or-equal, slanted2 is an integer and A* denotes the adjoint of A. Denote by image the set of all k-generalized projectors in image. In this paper, we show that any two homotopic k-generalized projectors are path connected and that there does not exist a segment image when P and Q are two different k-generalized projectors.