SOME CLASS OF NUMERICAL RADIUS PEAK n-LINEAR MAPPINGS ON lp-SPACES

초록

For n≥ 2 and a real Banach space E, £(nE: E) denotes the space of all continuous n-linear mappings from E to itself. Let (Formula presented) For T€ £(nE: E), we define (Formula presented) where v(T) denotes the numerical radius of T. T is called numerical radius peak mapping if there is [x*, (x<inf><inf>1</inf></inf>,…, x<inf><inf>n</inf></inf>)]€ Π(E) such that Nr(T) = {±[x*, (x<inf><inf>1</inf></inf>,…, x<inf><inf>n</inf></inf>)]}. In this paper, we investigate some class of numerical radius peak mappings in L(nl<inf><inf>p</inf></inf>: l<inf><inf>p</inf></inf>) for 1<p <∞. Let (a<inf><inf>j</inf></inf>)<inf><inf>j€ℕ</inf></inf> be a bounded sequence in ℝ such that sup<inf><inf>j€ℕ</inf></inf> | aj| > 0. Defne T€ £(nl<inf><inf>p</inf></inf>: l<inf><inf>p</inf></inf>) by (Formula presented) In particular is proved the following statements: 1. If 1<p <+∞ then T is a numerical radius peak mapping if and only if there is j<inf><inf>o</inf></inf>€ ℕ such that (Formula presented) 2. If p = 1 then T is not a numerical radius peak mapping in £(n l: l). © S. G. Kim, 2022

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