NUMERICAL RADIUS POINTS OF A BILINEAR MAPPING FROM THE PLANE WITH THE l1-NORM INTO ITSELF

초록

For n = 2 and a Banach space E we let Pi(E) = {[x*, x(1),..., x(n)] : x*(x(j)) = parallel to x*parallel to = parallel to x(j)parallel to = 1 for j = 1,..., n}. Let L(E-n : E) denote the space of all continuous n-linear mappings from E to itself. An element [x*, x(1),..., x(n)] is an element of Pi(E) is called a numerical radius point of T is an element of L(E-n : E) if |x*(T(x(1),..., x(n)))| = v(T), where v(T) is the numerical radius of T. Nradius(T) denotes the set of all numerical radius points of T. In this paper we classify Nradius(T) for every T is an element of L((2)l(2)(1) : l(1)(2)) in connection with Norm(T), where Norm(T) denotes the set of all norming points of T.

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