ar X iv : m at h / 99 11 13 3 v 1 [ m at h . O A ] 1 7 N ov 1 99 9 GEOMETRY OF OBLIQUE PROJECTIONS ∗ †
نویسنده
چکیده
Let A be a unital C∗-algebra. Denote by P the space of selfadjoint projections ofA. We study the relationship between P and the spaces of projections Pa determined by the different involutions #a induced by positive invertible elements a ∈ A. The maps φp : P → Pa sending p to the unique q ∈ Pa with the same range as p and Ωa : Pa → P sending q to the unitary part of the polar decomposition of the symmetry 2q − 1 are shown to be diffeomorphisms. We characterize the pairs of idempotents q, r ∈ A with ‖q − r‖ < 1 such that there exists a positive element a ∈ A verifying that q, r ∈ Pa. In this case q and r can be joined by an unique short geodesic along the space of idempotents Q of A.
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ar X iv : m at h / 99 11 13 3 v 2 [ m at h . O A ] 1 8 N ov 1 99 9 GEOMETRY OF OBLIQUE PROJECTIONS ∗ †
Let A be a unital C∗-algebra. Denote by P the space of selfadjoint projections ofA. We study the relationship between P and the spaces of projections Pa determined by the different involutions #a induced by positive invertible elements a ∈ A. The maps φp : P → Pa sending p to the unique q ∈ Pa with the same range as p and Ωa : Pa → P sending q to the unitary part of the polar decomposition of t...
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