C¤¡ALGEBRA MATRIX RANGES

The algebra of all bounded linear operators on a Hilbert space H is denoted by B(H). Let A be a C*-algebra with identity and a 2 A. If C¤(a) be the C*-algebra generated by fa; 1g, Hn, for positive integer n, the n¡dimensional Hilbert space and CP(C¤(a);Hn; 1) the set of all completely positive maps of C¤(a) into B(Hn) . In this paper we define C*-algebra n¡dimensional matrix range of a by Vn(a) := fʹ(a) : ʹ 2 CP(C¤(a);Hn; 1)g, and discuss some properties.