THE NORMING SET OF T ∈ Ls (Formula presented) FOR n = 3, 4, 5

초록

Let n ∈ N, n ≥ 2 and (E, ‖ · ‖) a Banach space. 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 (Formula presented) Norm(T) is called the norming set of T. Let (Formula presented)= R2 with the ℓ<inf>1</inf>-norm. In this paper, we characterize the norming set of T ∈ (Formula presented). Using this result, we completely describe the norming set of T ∈ L<inf>s</inf> ((Formula presented)) for n = 3, 4, 5, where L<inf>s</inf> (n (Formula presented) denotes the space of all symmetricn-linear forms onℓ21.. © Palestine Polytechnic University-PPU 2024.

키워드