EUDML | Differential geometry of the family of $R_k$’s in $R_n$ and of the family of totally geodesic $S_{k-1}$’s in $S_{n-1}$ of positive curvature

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Displaying similar documents to “Differential geometry of the family of $R_{k}$ ’s in $R_{n}$ and of the family of totally geodesic $S_{k - 1}$ ’s in $S_{n - 1}$ of positive curvature”

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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 different involutions $_{a}$ induced by positive invertible elements a ∈ A. The maps $φ : P \to P_{a}$ sending p to the unique $q \in P_{a}$ with the same range as p and $Ω_{a} : P_{a} \to P_{a}$ 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|| <...

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