THE NORMING SETS OF L(2d*(1, w)2)

Abstract

Let 𝑛 ∈ ℕ. An element ( x 1 , … , x 𝑛 ) ∈ E n is called a norming point of T ∈ ( n E ) if ‖ x 1 ‖ = ⋯ = ‖ x n ‖ = 1 and | T ( x 1 , … , x n )| = ‖ T ‖, where ( n E ) denotes the space of all continuous n -linear forms on E . For T ∈ ( n E ), we define Norm( T ) = {( x 1 , … , x n ) ∈ E n ∶ ( x 1 , … , x n ) is a norming point of T }. Norm( T ) is called the norming set of T . We classify Norm( T ) for every T ∈ ( 2 𝑑 ∗ (1, w ) 2 ), where 𝑑 ∗ (1, w ) 2 = ℝ 2 with the octagonal norm of weight 0 < w < 1 endowed with .