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Geometry of oblique projections

E. Andruchow, Gustavo Corach, D. Stojanoff (1999)

Studia Mathematica

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 P a sending p to the unique q P a with the same range as p and Ω a : P a 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|| < 1 such that...

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