On the convex set of completely positive linear maps in
matrix algebras
1997 ◽
Vol 122
(1)
◽
pp. 45-54
◽
Keyword(s):
Rank One
◽
Let PI (respectively CPI) be the convex compact set of all unital positive (respectively completely positive) linear maps from the matrix algebra Mm([Copf ]) into Mn([Copf ]). We show that maximal faces of CPI correspond to one dimensional subspaces of the vector space Mm, n([Copf ]). Furthermore, a maximal face of CPI lies on the boundary of PI if and only if the corresponding subspace is generated by a rank one matrix.
2013 ◽
Vol 25
(02)
◽
pp. 1330002
◽
Keyword(s):
1996 ◽
Vol 39
(1)
◽
pp. 74-82
◽
Keyword(s):
1972 ◽
Vol 24
(3)
◽
pp. 520-529
◽
Keyword(s):
2019 ◽
Vol 40
(10)
◽
pp. 1549-1568
2007 ◽
Vol 47
(10)
◽
pp. 1589-1602
◽
Keyword(s):
2015 ◽
Vol 47
(1)
◽
pp. 455-476
◽
The structure of $C^*$-extreme points in spaces of completely positive linear maps on $C^*$-algebras
1998 ◽
Vol 126
(5)
◽
pp. 1467-1477
◽
2019 ◽
Vol 59
(7)
◽
pp. 1098-1104
Keyword(s):