Abstract. In this paper, we give an order theoretic characterization for order unit norms in the matrix order context. Using this characterization, we give a matix order theoretic definition for matrix order unit spaces, and show that this definition is more general that of Choi and Effros. We introduce bases in the matrix order context and characterize them. We also introduce matrix base normed spaces and obtain a canonical structure for these spaces.
1991 Mathematics Subject Classification. 46L05.
Key words and phrases. Matrix order unit space, matrix base normed space, matricially normed space.