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Zbl 0852.46050
Kye, Seung-Hyeok
Facial structures for the positive linear maps between matrix algebras.
(English)
[J] Can. Math. Bull. 39, No.1, 74-82 (1996). ISSN 0008-4395; ISSN 1496-4287/e

Summary: Let $\cal P$ denote the convex set of all positive linear maps from the matrix algebra $M_n(\bbfC)$ into itself. We construct a join homomorphism from the complete lattice ${\cal F}({\cal P})$ of all faces of $\cal P$ into the complete lattice ${\cal J}({\cal V})$ of all join homomorphisms between the lattice $\cal V$ of all subspaces of $\bbfC^n$. We also characterize all maximal faces of $\cal P$.
MSC 2000:
*46L05 General theory of C*-algebras
06B99 Lattices

Keywords: positive linear maps; matrix algebra; complete lattice; maximal faces

Cited in: Zbl 0960.46036

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