We show that noncommutative Lp-spaces satisfy the axioms of the (nonunital) operator system with a dominating constant 2 1 p . Therefore, noncommutative Lpspaces can be embedded into BpHq 2 1 p -completely isomorphically and complete order isomorphically. 1. Introducton A unital involutive subspace of BpHq had been abstractly characterized by Choi and Effros [CE]. Their axioms are based on obse...

On the space l of p-summable sequences (of real numbers), one can derive a norm from the 2-norm as indicated by Gunawan [6]. The purpose of this note is to establish the equivalence between such a norm and the usual norm on l. We show that our result is useful in understanding the topology of l as a 2-normed space.