ABSTRACT. There a.re two known 2-norms defined on the space of p-summable sequences of real numbers. The first 2-norm is a special case of Gahler's for­ mula [Niathematische Nachrichten, 1964], while the second is due to Gunawan [Bulletin of the Australian Mathematical Society, 2001]. The ai1n of this paper is to define a new 2-norm on eP and prove the equivalence among these three 2-norms.