ON BIRKHOFF THEOREM FOR DOUBLY STOCHASTIC COMPLETELY POSITIVE MAPS OFMATRIX ALGEBRAS

Authors
LANDAU LJ STREATER RF
Citation
Lj. Landau et Rf. Streater, ON BIRKHOFF THEOREM FOR DOUBLY STOCHASTIC COMPLETELY POSITIVE MAPS OFMATRIX ALGEBRAS, Linear algebra and its applications, 193, 1993, pp. 107-127
Citations number
19
Categorie Soggetti
Mathematics,Mathematics
Journal title
Linear algebra and its applications → ACNP
ISSN journal
00243795
Volume
193
Year of publication
1993
Pages
107 - 127
Database
ISI
SICI code
0024-3795(1993)193:<107:OBTFDS>2.0.ZU;2-V
Abstract
A study is made of the extreme points of the convex set of doubly stoc hastic completely positive maps of the matrix algebra M(n). If n = 2 t he extreme points are precisely the unitary maps, but if n greater-tha n-or-equal-to 3 there are nonunitary extreme points, examples of which are exhibited. A tilde operation is defined on the linear maps of M(n ) and used to give an elementary derivation of a result of Kummerer an d Maassen.