Norm attaining bilinear forms of L(2d∗(1,w)2) at given vectors

초록

For given unit vectors x1,···,xn of a real Banach space E, we de ne NA(L(nE))(x1, · · ·, xn) = {T ∈ L(nE): |T(x1, · · ·, xn)| = kT k = 1}, where L(nE) denotes the Banach space of all continuous n-linear forms on E endowed with the norm kT k = sup<inf>kxkk</inf><inf>=1,1</inf>≤k≤<inf>n</inf> |T(x1,..., xn)|. In this paper, we classify NA(L(2d∗(1, w)2))(Z1, Z2) for unit vectors Z1, Z2 ∈ d∗(1, w)2 where d∗(1, w)2 = R2 with the norm of weight 0 < w < 1 endowed with k(x, y)k<inf>d∗</inf><inf>(1,w)</inf> = max n |x|, |y|, |x<inf>1+</inf>|+<inf>w</inf>|y|o © S. G. KIM, 2023.

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