International Journal of Mathematics and Mathematical Sciences
Volume 30 (2002), Issue 1, Pages 31-37
doi:10.1155/S016117120200697X

An n×n matrix of linear functionals of C∗-algebras

Abstract

We show that any bounded matrix of linear functionals [fij]:Mn(A)→Mn(ℂ) has a representation fij(a)=〈Tπ(a)xj,xi〉, a∈A, i,j=1,2,…,n, for some representation π on a Hilbert space K and an n vectors x1,x2,…,xn in K.