Cones arising from C*-subalgebras and complete positivity Academic Article uri icon

abstract

  • Let B ⊆ A be an inclusion of C*-algebras. Then B is said to norm A if, for each X ∈ double-struck Mn(A), ∥X∥ = sup{∥RXC∥: R* C ∈ Coln(B), ∥R∥, ∥C∥ ≤ 1}. In this paper we introduce and study the cones {X ∈ double-struck Mn(A)sa: C*XC ≥ 0 for C ∈ Coln(B)}, n ≥ 1. These are shown to coincide with the standard positive cones precisely when B norms A, and we apply this to obtain automatic complete positivity of certain positive maps between C*-algebras. © 2008 Cambridge Philosophical Society.

author list (cited authors)

  • POP, F., & SMITH, R. R.

citation count

  • 4

complete list of authors

  • POP, FLORIN||SMITH, ROGER R

publication date

  • July 2008