Numerical radius peak multilinear mappings on ℓ1

초록

For n >= 2 and a Banach space E, L(nE : E) denotes the space of all continuous n-linear mappings from E to itself. We let pi(E)={[x*, x1, ... ,xn] :x*(xj)= parallel to x*parallel to = parallel to xj parallel to = 1 for j = 1, ..., n }. An element [x*, x1, ... , xn] is an element of pi(E) is called a numerical radius point of T is an element of L(nE : E) if |x*(T(x1, ... , xn))| = v(T), ⠌⠌ where the numerical radius v(T) = sup[y*,y1,...,yn]is an element of pi(E) y*⠐T(y1,...,yn)⠑ ⠌. For T is an element of L(nE : E), we define Nradius(T) = {[x*, x1, ... , xn] is an element of pi(E) : [x*, x1, ... ,xn] is a numerical radius point of T}. Nradius(T) is called the set of all numerical radius points for T. T is called numerical radius peak n-linear mapping if Nradius(T) = {+/-[x*, x1, ... , xn]}. In this paper we investigate Nradius(T) for every T is an element of L(nl1 : l1) and characterize all numerical radius peak multilinear mappings in L(nl1 : l1), where l1 is a real or complex space.

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