NORM-PEAK MULTILINEAR MAPPINGS ON Rn WITH A CERTAIN NORM

초록

Let n >= 2 A continuous n-linear mapping T from a Banach space E into a Banach space F is called norm-peak if there is unique (x(1),..., x(n)) E-n such that || x (1) ||=***= ||x(n)|| = 1 and T' attains its norm only at (+/- x(1),..., x(n)).<br /> Let R-||.||.(n) R-n with a norm satisfying that {W-1,..., W-n} forms a basis and the set of all extreme points of B(Rn ||.|| )is {+W-1,..., W-n}.<br /> In this note, we characterize all norm-peak multilinear mapping from R-||.||.(n). into F.

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