Linear Maps betweenC*-Algebras Whose Adjoints Preserve Extreme Points of the Dual Ball
✍ Scribed by Louis E. Labuschagne; Vania Mascioni
- Publisher
- Elsevier Science
- Year
- 1998
- Tongue
- English
- Weight
- 464 KB
- Volume
- 138
- Category
- Article
- ISSN
- 0001-8708
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✦ Synopsis
We give a structural characterization of linear operators from one C*-algebra into another whose adjoints map extreme points of the dual ball onto extreme points. We show that up to a V-isomorphism, such a map admits of a decomposition into a degenerate and a non-degenerate part, the non-degenerate part of which appears as a Jordan V-morphism followed by a rotation'' and then a reduction. In the case of maps whose adjoints preserve pure states, the degenerate part does not appear, and the rotation'' is but the identity. In this context the results concerning such pure state preserving maps depend on and complement those of Sto% rmer [1963, Acta Math. 110, 233 278, 5.6 and 5.7]. In conclusion we consider the action of maps with ``extreme point preserving'' adjoints on some specific C*-algebras.