Positive Linear Maps on C^*-Algebras

Abstract

The objective of this paper is to give some concrete distinctions between positive linear maps and completely positive linear maps on C * -algebras of operators. Herein, C * -algebras possess an identity and are written in German type . Capital letters A, B, C stand for operators, script letters for vector spaces, small letters x, y, z for vectors. Capital Greek letters Φ, Ψ stand for linear maps on C * -algebras, small Greek letters α, β, γ for complex numbers. We denote by the collection of all n × n complex matrices. ( ) = ⊗ is the C * -algebra of n × n matrices over .