THE NORMING SETS OF L(mln1)

초록

Let n is an element of N, n >= 2. An element (x(1), ... , x(n)) is an element of E-n is called a norming point of T is an element of L(E-n) if parallel to x(1)parallel to = ... = parallel to x(n)parallel to = 1 and vertical bar T(x(1), ... , x(n))vertical bar = parallel to T parallel to, where L(E-n) denotes the space of all continuous n-linear forms on E. For T is an element of L(E-n), we define Norm(T) = {(x(1), ... , x(n)) is an element of E-n: (x(1), ... , x(n)) is a norming point of T}. The set Norm(T) is called the norming set of T. For m is an element of N, m >= 2, we characterize Norm(T) for any T is an element of L((m)l(1)(n)), where l(1)(n) = R-n with the l(1)-norm. As applications, we classify Norm(T) for every T is an element of L((m)l(1)(n)) with n = 2, 3 and m = 2.