# Geometry of oblique projections

E. Andruchow; Gustavo Corach; D. Stojanoff

Studia Mathematica (1999)

- Volume: 137, Issue: 1, page 61-79
- ISSN: 0039-3223

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topAndruchow, E., Corach, Gustavo, and Stojanoff, D.. "Geometry of oblique projections." Studia Mathematica 137.1 (1999): 61-79. <http://eudml.org/doc/216675>.

@article{Andruchow1999,

abstract = {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.},

author = {Andruchow, E., Corach, Gustavo, Stojanoff, D.},

journal = {Studia Mathematica},

keywords = {-algebra; oblique projections; idempotents; geodesic},

language = {eng},

number = {1},

pages = {61-79},

title = {Geometry of oblique projections},

url = {http://eudml.org/doc/216675},

volume = {137},

year = {1999},

}

TY - JOUR

AU - Andruchow, E.

AU - Corach, Gustavo

AU - Stojanoff, D.

TI - Geometry of oblique projections

JO - Studia Mathematica

PY - 1999

VL - 137

IS - 1

SP - 61

EP - 79

AB - 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.

LA - eng

KW - -algebra; oblique projections; idempotents; geodesic

UR - http://eudml.org/doc/216675

ER -

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