Norm attaining bilinear forms on the plane with the l1-norm

초록

For given unit vectors x(1), middot middot middot , x(n) of a real Banach space E, we define NA(L(E-n))(x(1), middotmiddotmiddot , x(n)) = {T is an element of L(E-n) : |T(x(1), middot middot middot , x(n))| = | | T| | = 1}, where L(E-n) denotes the Banach space of all continuous n-linear forms on E endowed with the norm | | T| | = sup(| | xk| | =1,1 <= k <= n )|T(x(1),. . . , x(n))|. In this paper, we classify NA(L((2)l(1)(2)))((x(1), x(2)), (y(1), y(2))) for unit vectors (x(1), x(2)), (y(1), y(2)) is an element of l(1)(2), where l(1)(2) =R-2 with the l(1)-norm.

키워드