Positivity and Norms
Following some lines of joint work with A.
S. Householder, the character and use of algebraic 
methods in the theory of norms is demonstrated.  New results
concerning norms with values in an Archimedian 
vector lattice (not necessarily being totally ordered)
are given, in particular for the generalization 
of order unit norms, L-norms and M-norms.  An example
of application to operator norms is given concerning 
contraction properties of positive operators.
CACM January, 1975
Bauer, F. L.
