THERE ARE NO NUMERICAL RADIUS PEAK n-LINEAR MAPPINGS ON c0

초록

For n > 2 and a real Banach space E, G(nE : E) denotes the space of all continuous n-linear mappings from E to itself. Let & pi;(E) = {[x*, (x1, . . . , xn)] : x*(xj) = IIx*II = IIxjII =1 for j =1, ... , n }. An element [x*, (x1, ... , xn)] E & pi;(E) is called a numerical radius point of T E G(nE : E) if |x*(T(x1,. . . ,xn))| = v(T), where the numerical radius y*� v(T) = sup[y*,y1,...,yn]E & pi;(E) T(y1,... , yn)) . For T E G(nE : E), we define Nradius(T) = {[x*, (x1, ... , xn)] E & pi;(E) : [x*, (x1, ... , xn)] is a numerical radius point of T }. T is called a numerical radius peak n-linear mapping if there is a unique [x*, (x1, .. . , xn)] E & pi;(E) such that Nradius(T) = {& PLUSMN;[x*, (x1, ... ,xn)]}. In this paper we present explicit formulae for the numerical radius of T for every T E G(nE : E) for E = c0 or loo. Using these formulae we show that there are no numerical radius peak mappings of G(nc0 : c0).

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