# Orbits of Positive Operators from a Differentiable Viewpoint

Orbits of Positive Operators from a Differentiable Viewpoint Let $$\mathcal{A}$$ be a unital C*-algebra and G the group of units of $$\mathcal{A}$$ . A geometrical study of the action of G over the set $$\mathcal{A}$$ + of all positive elements of $$\mathcal{A}$$ is presented. The orbits of elements with closed range by this action are provided with a structure of differentiable homogeneous space with a natural connection. The orbits are partitioned in ''components'' which also have a rich geometrical structure. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

# Orbits of Positive Operators from a Differentiable Viewpoint

, Volume 8 (1) – Oct 21, 2004
18 pages

/lp/springer_journal/orbits-of-positive-operators-from-a-differentiable-viewpoint-fXd8x9e1xg
Publisher
Subject
Mathematics; Fourier Analysis; Operator Theory; Potential Theory; Calculus of Variations and Optimal Control; Optimization; Econometrics
ISSN
1385-1292
eISSN
1572-9281
D.O.I.
10.1023/B:POST.0000023202.40428.a8
Publisher site
See Article on Publisher Site

### Abstract

Let $$\mathcal{A}$$ be a unital C*-algebra and G the group of units of $$\mathcal{A}$$ . A geometrical study of the action of G over the set $$\mathcal{A}$$ + of all positive elements of $$\mathcal{A}$$ is presented. The orbits of elements with closed range by this action are provided with a structure of differentiable homogeneous space with a natural connection. The orbits are partitioned in ''components'' which also have a rich geometrical structure.

### Journal

PositivitySpringer Journals

Published: Oct 21, 2004

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