Geometry of Oblique Projections
نویسنده
چکیده
Let A be a unital C-algebra. Denote by P the space of selfadjoint projections of A. We study the relationship between P and the spaces of projections P a determined by the diierent involutions # a induced by positive invertible elements a 2 A. The maps ' p : P ! P a sending p to the unique q 2 P a with the same range as p and a : P a ! P sending q to the unitary part of the polar decomposition of the symmetry 2q ? 1 are shown to be diieomorphisms. We characterize the pairs of idempotents q; r 2 A with kq ? rk < 1 such that there exists a positive element a 2 A verifying that q; r 2 P a. In this case q and r can be joined by an unique short geodesic along the space of idempotents Q of A.
منابع مشابه
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