The Norming Set of a Bilinear Form on R2 with the Octagonal Norm

초록

An element (x(1),..., x(n)). En is called a norming point of T is an element of L(E-n) if ||x(1)|| = center dot center dot center dot =||x(n)|| = 1 and |T(x(1),..., x(n))| = ||T||, 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} Let R-o(w)(2) denote R-2 with the octagonal norm with weight 0 < w not equal 1 ||(x, y)||(o(w)) = max { |x| + w|y|, |y| + w|x|}. In this paper we classify Norm (T) for every T is an element of L(R-2(o(w))2) with weight 0 < w not equal 1.

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