The norming sets of ℒ( 2ℓ1 2) and ℒS( 2ℓ1 3)

Abstract

Let n ∈ N. An element (x1, . . . , xn) ∈ E n is called a norming point of T ∈ ℒ ( nE) if ∥x1∥ = · · · = ∥xn∥ = 1 and |T(x1, . . . , xn)| = ∥T∥, where ℒ( nE) denotes the space of all continuous n-linear forms on E. For T ∈ ℒ ( nE), we define Norm(T) = { n (x1, . . . , xn) ∈ En : (x1, . . . , xn) is a norming point of T } . Norm(T) is called the norming set of T. We classify Norm(T) for every T ∈ ℒ ( 2ℓ12) or ℒs ( 2ℓ13), where ℓ1n = ℝn with the ℓ1-norm.