The Norming Sets ofLml1n

Let n ∈ ℕ, n ≥ 2 . An element ( x 1 ,…, x n ) ∈ E n is called a norming point of T ∈ L n E if || x 1 || = … = || x n || = 1 and |T ( x 1 , … , x n ) | = || T ||, where ℒ( n E ) denotes the space of all continuous n -linear forms on E. For T ∈ ℒ ( n E ), we define Norm T = x 1 , ⋯ , x n ∈ E n : x 1 , ⋯ , x n is a norming point of T . The set Norm( T ) is called the norming set of T. For m ∈ ℕ , m ≥ 2, we characterize Norm( T ) for any T ∈ L m l 1 n , where l 1 n = R n with the l 1 -norm. As applications, we classify Norm( T ) for every T ∈ L m l 1 n with n = 2, 3 and m = 2 .