THE NORMING SETS OF L(2 l21) and Ls (2 l31)

초록

Let n ∈ N. An element (x<inf>1</inf>, …, x<inf>n</inf>) ∈ En is called a norming point of T ∈ L(n E) if ∥x<inf>1</inf> ∥ = · · · = ∥x<inf>n</inf> ∥ = 1 and |T (x<inf>1</inf>, …, x<inf>n</inf>)| = ∥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<inf>1</inf>, …, x<inf>n</inf>) ∈ En: (x<inf>1</inf>, …, x<inf>n</inf>) is a norming point of T } . Norm(T) is called the norming set of T . We classify Norm(T) for every T ∈ L(2 l1)2 or L<inf>s</inf> (2 l1),3 where l1n = Rn with the l<inf>1</inf>-norm. © 2022, Transilvania University of Brasov 1. All rights reserved.

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