Abstract
Let B ( H ) be the set of all bounded linear operators on a Hilbert space H. An operator A ∈ B ( H ) is said to be a k-generalized projector if A k = A ∗ , where k ⩾ 2 is an integer and A ∗ denotes the adjoint of A. Denote by B ( H ) k - GP the set of all k-generalized projectors in B ( H ) . In this paper, we show that any two homotopic k-generalized projectors are path connected and that there does not exist a segment [ P , Q ] ⊆ B ( H ) k - GP when P and Q are two different k-generalized projectors.
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