Geometry of oblique projections
Studia Mathematica, Tome 137 (1999) no. 1, pp. 61-79
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
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 there exists a positive element a ∈ A satisfying $q,r ∈ P_a$. In this case q and r can be joined by a unique short geodesic along the space of idempotents Q of A.
@article{10_4064_sm_137_1_61_79,
author = {E. Andruchow and and },
title = {Geometry of oblique projections},
journal = {Studia Mathematica},
pages = {61--79},
publisher = {mathdoc},
volume = {137},
number = {1},
year = {1999},
doi = {10.4064/sm-137-1-61-79},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm-137-1-61-79/}
}
E. Andruchow; ; . Geometry of oblique projections. Studia Mathematica, Tome 137 (1999) no. 1, pp. 61-79. doi: 10.4064/sm-137-1-61-79
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