1996/04/06 by Louis E. Labuschagne, Vania Mascioni, Labuschagne, Louis E. +1
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models
paper · pdf · doi:10.48550/arxiv.math/9604213
We give a structural characterisation of linear operators from one C^\∗%\n-algebra into another whose adjoints map extreme points of the dual ball onto\nextreme points. We show that up to a \∗-isomorphism, such a map admits of a\ndecomposition into a degenerate and a non-degenerate part, the non-degenerate\npart of which appears as a Jordan \∗-morphism followed by a ``rotation''\nand then a reduction. In the case of maps whose adjoints preserve pure states,\nthe degenerate part does not appear, and the ``rotation'' is but the identity.\nIn this context the results concerning such pure state preserving maps depend\non and complof St o rmer [St o 2; 5.6 & 5.7]. In conclusion we consider the\naction of maps with ``extreme point preserving'' adjoints on some specific\nC^\∗-algebras.\n